Morphodynamic evolution of experimental cohesive deltas

Morphodynamic evolution of experimental cohesive deltas

D. C. J. D. Hoyal1 and B. A. Sheets1,2

Received 2 August 2007; revised 12 January 2009; accepted 29 January 2009; published 23 April 2009.

[1] Here we describe new techniques for creating river-dominated (birds foot) deltas withstrong channelization in the laboratory. The key to achieving strong self-channelization isthe addition of a commercially available polymer to the sediment mixture. This polymerenhances the substrate strength increasing the critical erosion stress, an importantgeomorphic threshold. More importantly it increases the rate of cohesion onset to accountfor increased rates of morphodynamic evolution in small-scale experiments. A cyclicpattern of delta evolution is observed. The delta ‘‘avulsion cycle’’ begins with channelavulsion, erosion, and channel elongation and ends with channel backfilling andabandonment. This cycle appears to be universal but is subject to a range of controls,including sediment size distribution, sediment concentration, substrate cohesiveness, andFroude number. We propose that the observed depositional cycle is characteristic of anavulsion mechanism that is more complex than current models of fluvial systems, whichgenerally explain avulsion probability as an upstream effect dependent on channelsuperelevation or levee slope. The experiments suggest that in many distributary channelsystems, including deltas, alluvial, and deep water fans, downstream mediated topographiceffects or ‘‘morphodynamic backwater effects’’ may dominate over upstream avulsionprocesses and control the surface mechanics and stratigraphy. The experimentalobservations are synthesized into a new depositional model for river-dominated deltaswhich emphasizes the importance of self-organization and feedback in delta surfaceevolution and stratigraphy.

Citation: Hoyal, D. C. J. D., and B. A. Sheets (2009), Morphodynamic evolution of experimental cohesive deltas, J. Geophys. Res.,

114, F02009, doi:10.1029/2007JF000882.

1. Introduction

[2] Deltas, ubiquitous and dynamic features of theworld’s coastlines, are important sites for coastal citiesand have been heavily engineered for ports and rivernavigation. In addition, because of their high depositionand subsidence rates, ancient deltas often contain significanthydrocarbon reserves [e.g., Ainsworth et al., 1999; Bohacsand Suter, 1997]. Recently, deltas have attracted increasedattention because of coastal land loss issues related to stormsurge and sea level rise associated with long-term climatechanges.[3] Despite their great economic and social importance

our current understanding of delta surface processes, evo-lution, and related self-organization remains incomplete.This lack of understanding is largely a result of the intrinsiccomplexity of the processes involved, our inability toobserve them over the long timescales necessary for naturaldelta evolution (e.g., 103–104 years for the Mississippidelta) and difficulties associated with collecting data inthe coastal transition zone. Consequently, even the simplest

end-member case, of a homopycnal, river-dominated deltaunder steady fluvial input, is not particularly well under-stood. This scenario, generally best approximated in natureby a river entering a small lake, has important implicationsas a baseline case for understanding all river-dominateddeltas, and arguably provides insights into their wave- andtide-dominated cousins as well [e.g., Swenson, 2005;Jerolmack and Swenson, 2007].[4] A delta is a variant of an alluvial fan where the

sediment transport is significantly diminished at the coast(a downstream control) by the presence of standing water[Gilbert, 1884] and, like most alluvial fans, has a complexnetwork of distributary channels on its surface [Olariu andBhattacharya, 2006]. Perhaps the best-studied example,arguably the archetype, of an avulsing river-dominated deltais the Mississippi, whose Holocene history has been in-tensely scrutinized and has been a source for many impor-tant scientific concepts on delta evolution [Bates, 1953; Fisket al., 1954; Gould, 1970; Morgan, 1970; Wright andColeman, 1973; Wright, 1977] (also see Roberts [1997]for a comprehensive historical perspective). This body ofwork on the Mississippi led to the concept of delta lobeswitching, ‘‘the fundamental depositional style that hasshaped coastal environments of the Mississippi delta plainthrough Holocene time’’ [Roberts, 1997, p. 606]. Themechanism invoked to explain lobe switching is entirelyautogenic. It begins with stream capture and the establish-

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, F02009, doi:10.1029/2007JF000882, 2009

1ExxonMobil Upstream Research Company, Houston, Texas, USA.2Now at School of Oceanography, University of Washington, Seattle,

Washington, USA.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2007JF000882

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ment of a well-defined channel network (the ‘‘fluvially-dominated regressive phase’’) and ends with a ‘‘marine-dominated transgressive phase’’ involving marine reworkingto form beaches, spits, barrier islands and, finally, submarineshoals as a result of lobe abandonment and subsidence[Roberts, 1997].[5] The largest lobes of the Mississippi delta form in 1–

2 ka cycles, far faster than the Holocene signal of sea levelvariation. Roberts [1997] calls this the ‘‘delta cycle,’’ whichprovides the context for the development of a range ofmorphodynamic structures observed on the present-dayLouisiana coast. He suggests that the delta cycle is, in fact,a series of nested cycles that explain lobe formation over arange of scales from crevasse splays (<5 m thick,�100 years), through subdeltas (e.g., bayhead deltas) tothe largest delta lobes (10–100 m thick, �1000 years).Avulsion cycles are also well documented on other largeriver-dominated deltas, most notably the Rhine-Meuse [e.g.,Stouthamer and Berendsen, 2001].[6] Avulsion cycles are a universal feature of distributary

channel systems, including fluvial systems [Smith et al.,1989; Davies-Vollum and Kraus, 2001; Farrell, 2001;Slingerland and Smith, 2004], alluvial fans [Hooke, 1967]and submarine fans [Normark, 1970; Flood et al., 1991;Gardner and Borer, 2000]. Channels develop because sheetflow is fundamentally inefficient. Increased flow depth inchannels leads to smaller bed surface areas and thereforeless bed friction per unit flow volume. As a result, followingavulsion there is a strong tendency for sheet flows toquickly channelize and extend basinward. Avulsion cyclesare a consequence of this channel instability (positivefeedback) and associated negative feedback mechanisms,but are subject to a range of controls that alter the channelcharacter and dynamics. Apart from cohesiveness, thecontrolling variables include emergent properties like slope,Froude number and intrinsic structural scales (e.g., channelwidth and depth), which depend on imposed water dis-charge, grain size and sediment concentration [e.g., Paola,2000]. Froude number is important because it governshydrodynamic information transfer and therefore morpho-dynamic feedback along channels. In addition it controlsthe existence of specific hydraulic and morphodynamicstructures.[7] One way to study these processes and their controls is

through the formation of small-scale physical models ofriver-dominated deltas in the laboratory. Unfortunately pastexperiments have been unable to reproduce the full range ofcomplexity observed in natural deltas because of 2-Dlimitations [Jopling 1965], poorly developed, overly mobilechannels [Shieh et al., 2001] and Froude supercritical flow[Sheets et al., 2007]. Previous studies have used simplenoncohesive sand mixtures [e.g., Shieh et al., 2001; Sheetset al., 2002]. These may be analogous to coarse-grained(gravelly, Gilbert-type) deltas and alluvial fans, with highlymobile channels and weak channelization (large wetted areato total area). Weak channelization, however, limits theability to generate complex river-dominated deltas at theexperimental scale. For example, the experiments of Shiehet al. [2001], while quantitatively documenting the earlystages of mouth bar extension and widening when fed by afixed inlet, were unable to develop the later stages ofmorphodynamic evolution associated with self-formed

channels. Noncohesive deltas express a smoother coastlinedue to the diffuse effect of faster channel migration [e.g.,Shieh et al., 2001; Sheets et al., 2007].[8] An experimental innovation described in this paper

enables strong channelization (small channel width, slowchannel migration, low-wetted area) at low Froude number,generating more realistic channel and shoreline patterns thatapproach the complexity of large-scale birds foot deltas likethe Mississippi. The key to increased complexity is en-hanced cohesion through the addition of an artificial poly-mer which increases the range of natural morphodynamicprocesses that can be reproduced. In real deltas it isexpected that most, or at least some of, these cohesiveeffects are imparted by vegetation.[9] The specific role of the polymer in experimental

channel development remains equivocal but is likely to beassociated with either transport thresholds or kinetics. Thepolymer increases substrate strength, enhancing hysteresisbetween deposition and erosion and increasing the criticalerosive shear stress, an important geomorphic threshold[Schumm et al., 1987; Kim et al., 2006]. Perhaps moreimportantly it increases the rate of cohesion onset to matchfast morphodynamic reaction rates in small-scale experi-ments. These rates are significantly larger than naturalsystems because of small channel depths and relativelylarge topographic growth rates associated with high sedi-mentation rates (i.e., high-sediment concentration) [e.g.,Bryant et al., 1995, Tornqvist and Bridge, 2002]. Sucheffects are complex and poorly understood requiring furthertheoretical and experimental investigation. Ultimately, a fullunderstanding of the influence of cohesion on channel crosssection, channel pattern, and the evolution of distributarychannel networks awaits the development of a comprehen-sive theory like that developed for sand and gravel bedrivers [e.g., Parker, 1978].[10] In the meantime systematic empirical trends ob-

served from controlled experiments may shed some lighton these relationships. The cohesive experiments are com-pared to geometrically simpler experiments with less cohe-sion (e.g., ‘‘weakly cohesive’’ case with polymer but noclay) and noncohesive systems (e.g., pure sand) undersimilar conditions (steady forcing, similar grain size, nobase level changes) enabling us to understand the effects ofvariable cohesion. In the cohesive deltas efficient routing ofsediment and water through well-developed spatially andtemporally persistent channels promotes low top set slopesand substantially subcritical Froude numbers. In contrast,inefficient sediment transport in noncohesive deltas due tocoarser sediment, high sediment loads and inefficient sheetflow, develops steep Froude supercritical fan deltas that arestarved of river load at the coast [e.g., Sheets et al., 2007;Orton and Reading, 1993; Postma, 1990; Schumm et al.,1987]. Sediment transport in these supercritical fans and fandeltas is typically disrupted by hydraulic jumps, whichshorten the length scale and lifespan of the channels [e.g.,Sheets et al., 2002; W. E. Weaver, Experimental study ofalluvial fans, unpublished Ph.D. dissertation, Colorado StateUniversity, 1984].[11] The primary objective of this research was to develop

improved depositional models of river-dominated deltasunder purely autogenic conditions. Current conceptualmodels of river-dominated deltas [e.g., Syvitski et al.,

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2005] are based on upstream avulsion mechanisms in fluvialsystems [e.g., Mohrig et al., 2000; Slingerland and Smith,2004]. They do not include feedbacks in the distributarychannel system or the effects of differences in cohesion.Here we propose an alternative depositional model, wheredownstream controls dominate delta avulsion and avulsioncycles, and introduce the idea of upstream propagating‘‘morphodynamic backwater’’ effects. These propagatethrough the distributary channel system and lead to strongspatial and temporal correlations in surface events andstrong spatial organization of the stratigraphy. At present,observations documenting downstream control on avulsionin deltas are rather scarce [Bhattacharya et al., 2001;Bhattacharya, 2006].

2. Experimental Methods

[12] The results and observations presented in this paperare drawn from seven experiments with various degrees ofcohesion (Table 1). The experiments were conducted at theExxonMobil Upstream Research Company in a 5� 3� 1 mdeep tank. The inlet condition in all experiments was a fixedchannel 3.81 cm wide and 20 cm deep (Figure 1) located atthe center of a wall (Agg2, long wall; other experiments,short wall). From this inlet, the deltas were free to expandradially, over a 180 degree angle. The basin floor was a flatand horizontal plate supported from below, with 20 cmspaces between the tank sidewalls and the plate. As a result,the deltas could prograde off the edges of the plate into‘‘deep water’’ if allowed to grow large enough, but hydrau-lic wall effects were kept to a minimum. Base level (basinwater depth) was held constant using a weir system (6.35 cmabove the flat plate for all experiments). As the deltaaggraded, the bed of the inlet channel was free to aggrade,thereby raising the inlet point.[13] Sediment and water were mixed outside the basin

and delivered at a fixed rate through the inlet channel at lowconcentrations (�1:500 for Agg1 and Agg2; for others seeTable 1). The cohesive sediment mixture comprises a nearuniform distribution of sediment grades ranging from ben-tonite clay to coarse sand (Figure 2), combined with a smallamount (approximately 100 g/50 kg sediment) of a com-mercially available shale stabilizing polymer developed foroil well drilling applications (i.e., New-Drill Plus, BakerHughes Inc). The sediment moves primarily as bed load inthe channels but a portion of the finer sediment that wouldnormally travel as suspended load is attached to the bed

load material by the action of the polymer. Coarse bed loadaccumulates in the channels and at the edge of channelmouth bars while the remaining fine suspended load accu-mulates overbank on the fluvial surface, (e.g., floodplaindeposits and levees), or in the offshore prodelta.[14] Various combinations of water discharge, cohesive-

ness and sediment discharge were simulated, includingcohesive low concentration (Agg1, Agg2, Delta9), cohesivehigh concentration (Delta7, Delta8) and lower cohesion(Delta14, Delta15). These experiments were part of ageneral investigation of controls on channelization (>20experiments) that led to the selection of particular experi-ments for further analysis. A number of experiments wererun with polymer but without clays in order to highlightinternal stratigraphy, which is obscured by clays in thecohesive experiments (Delta14, Delta15). While this ap-proach made the stratigraphy more visible, the polymerincreases sediment cohesiveness best with the presence ofclay and, consequently, these experiments developed geom-etries characteristic of sandy noncohesive deltas.[15] The cohesive Agg1 experiment was run continuously

for 200 h, producing a radially symmetric delta (Figure 1)approximately 11 cm thick and 5 cm above ‘‘sea level’’ atits thickest point. The most cohesive experiment, Agg2, wasrun intermittently over a 2 month period to facilitatetopographic scanning and consequently had the longestset-up time (Table 1). The Agg2 experiment ran for 150 h,not including pauses every 2 h for ultrasonic topographyscanning (approximately 4 h duration) (Figure 1). Through-out all experiments, digital images of delta evolution weretaken on 5 min intervals and rhodamine dye was injected on15 min intervals to aid in visualization of the flow patterns.A rapid series of images (6–8 at �1 sec interval) was takenduring dye release to enable measurement of flow velocityin the channels.[16] These experiments were not rigorously scaled be-

cause we do not understand all of the important scalingvariables, particularly those associated with cohesion. How-ever, given that natural sediment loads (total load), based onthe pre-1960 Mississippi River, [e.g., Syvitski, 2006] areapproximately 1/1000 that of the experiments (10�6 g/cc forthe Mississippi versus 10�3 g/cc for Delta9), and the grainsizes are about the same (both fine-medium sand), themorphodynamic reaction rate will be speeded up 106 timeson the basis of relative channel depths of 10 m and 1 cm,respectively. A similar speed-up factor (�106) is predictedon the basis of the ratio of a typical time for lobe growth in

Table 1. Experimental Conditionsa

DeltaExperiment

Qw

(l m�1)Qs

(l m�1)Runtime

(h) Fr ReWetted

Width (cm)Channel

Width (cm)Channel

Depth (cm) Width/DepthSediment Mixtureand Channel Pattern

7 20 0.08 14 2.67 390 76.2 7.62 0.14 45.40 Strongly cohesive, bifurcation dominant8 20 0.04 16 1.31 781 38.1 5.44 0.36 53.52 Strongly cohesive, bifurcation dominant9 20 0.02 72 0.59 5858 5.08 5.08 2.32 2.18 Strongly cohesive, avulsion dominant14 20 0.03 55 2.77 390 19.05 19.09 0.14 139.6 Weakly cohesive, bifurcation dominant15 20 0.03 38 1.90 390 10.88 10.88 0.17 62.43 Weakly cohesive, bifurcation dominantAgg1 10 0.01 200 0.61 3905 3.81 3.81 1.72 2.20 Strongly cohesive, avulsion dominantAgg2 10 0.01 150b 0.21 3905 3.81 3.81 3.46 1.09 Strongly cohesive, avulsion dominantMississippiRiver

1 � 1012 10�2 g/l – 0.1 107 10% 105 103 50–100 Cohesive, avulsion dominant

aHere Qs is sediment discharge, Qw is water discharge, Fr is Froude number, and Re is Reynolds number.bRun intermittently.


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the Mississippi (103 years) versus the experiments (�10 h).This dependence of morphodynamic reaction rate on sedi-mentation rate suggests that in addition to increased cohe-sion, decreased sedimentation rates are important for thepromotion of strong channelization, and this prediction isconfirmed experimentally in this study.[17] Our general scaling philosophy was to focus on the

aspects of scaling most likely to influence the mesoscalestructure such as channel patterns, applying a general‘‘similarity of process’’ methodology [Hooke, 1968]. Thisinvolved selecting for further study those experiments thatexhibited the best channel development (longest channels,smallest channel widths) within the dynamic regime ofinterest (e.g., low Froude number, bed load dominated).Additional criteria included the observation of geologicallyreasonable surface processes such as channel and barpatterns and realistic internal stratigraphy. The experimentaldeltas include compaction and related subsidence (�1 mm/day) such that flooding is observable on abandoned deltalobes. Even this small amount of differential subsidence cansignificantly influence subsequent morphodynamics in amanner similar to natural deltas, making the experiments auseful analog for the study of substrate-sedimentation

interactions [Morgan, 1970]. Another useful aspect of theexperimental cohesion is that it suppresses bed forms thatmight interfere with channel formation.[18] Table 1 includes typical nondimensional scaling

variables for the experiments as well as characteristic valuesfor fundamental emergent properties like channel width anddepth. Mean channel depth (d) is calculated on the basis ofthe known water discharge (Qw), estimates of flow velocity(v) in medial channels (i.e., 1/2 way down the delta from anadvancing dye front), and the total wetted width of theactive flow (W). Implicitly this approach assumes a rectan-gular channel cross section with area (A). Depth is calcu-lated from: A = Q/v and d = A/W. Losses through infiltrationor other processes were assumed to be negligible. Averagechannel width (w) is calculated by dividing the total medialwetted width (W) by the number of active channels (n).[19] Although the gross stratigraphic packaging and

large-scale spatial patterns of the experimental depositsappear to be remarkably similar to natural birdsfoot deltas[e.g., Roberts, 1997], a number of aspects of natural deltaicstratigraphy are not reproduced well in the experiments. Inparticular, natural deltas typically have larger proportions ofsuspended load and larger ocean depths which leads to the

Figure 1. Experimental arrangement and location of stratigraphic cross sections. (top) Overhead imageof Agg1 experimental delta with flow patterns highlighted in black and (bottom) perspective topographicscan taken at end of Agg2 experiment. Inlet position and positions of stratigraphic sections shown inFigure 10 denoted by vertical arrow and dashed lines, respectively. X, Y, and Z scales in cm.


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development of thicker and more depositionally diversemarine sections than are observed in the experiments.Consequently progradational (i.e., coarsening up) stratigra-phy is poorly represented in the experimental deltas. Fur-thermore, the experiments do not develop all of the detailedfacies observed in real deltas because of both the inability toproperly scale certain morphodynamic instabilities (e.g.,ripples or dunes, and in-channel bars) and the lack ofcertain processes, such as waves, tides and biologicalactivity. We assume that missing morphodynamic structurebelow the characteristic channel depth would add anotherlevel of detail without grossly affecting the general verticalgrain size patterns. That is, small-scale organization iscontrolled by (i.e., ‘‘slaved’’) to the large-scale structureand should not substantially affect the cycles described inthis paper [Haken, 1983; Werner, 1999].[20] In the heterogeneous delta environment, which spans

the transition between alluvial and marine processes, theflow is subject to diminishing gravity forces as the ambientfluid that surrounds the sediment-laden flow changes fromair (delta top) to water (delta front). At the coastline theeffective gravity forces and the dynamics are reset and as aresult the Froude number is commonly formulated differ-ently (and has a different value) in the subaerial andsubmarine realm. On the subaerial delta surface the Froudenumber can be approximated via the standard formulationfor open channel flows (Fr)

Fr ¼ Uffiffiffiffiffigh

p ; ð1Þ

where U is the depth-averaged velocity, g is gravitationalacceleration, and h the flow depth. Beyond the shoreline,the appropriate formulation for the Froude number in themarine realm is commonly called the densimetric Froudenumber (Fr0)

Fr0 ¼ Uffiffiffiffiffiffiffig0h

p ; ð2Þ

where

g0 ¼rf � ra��

��

rfg; ð3Þ

with ra the ambient fluid density, rf the density of rivermouth flow, and g0 the densimetric gravitational acceleration(reduced gravity).

3. Experimental Results

3.1. Channel and Mouth Bar Patterns as a Functionof Cohesion and Sediment Concentration

[21] The experiments demonstrate a range of channelpatterns as a function of sediment mixture cohesion andsediment concentration. In particular, cohesion and sedi-ment concentration influence both channel width and over-all wetted area on the delta top (Figure 3) by affecting bankstrength and sedimentation rate. Narrower and fewer chan-nels lead to increased channel depths and lower Froudenumbers, bringing the dynamic conditions in the experimentcloser to those in natural deltas (Table 1). For example, theexperiments shown in Figure 3 demonstrate that underidentical discharge and sediment mixture, increased con-centration leads to increased wetted width, decreased chan-nel depth and ultimately increased flow friction. This, inturn, leads to increased channel slopes and an increase inFroude number (see Figure 3 and Table 1).[22] On the basis of this exploratory study of delta

behavior, and the experiments of Sheets et al. [2002], werecognize three channel pattern regimes depending of themeasured Froude number and degree of cohesion. In orderof increasing sediment concentration, these are (1) persistentbranching channels, associated with cohesive sediments,subcritical flows (relatively strong gravitational forces)and relatively few, avulsive channels; (2) persistent radiat-ing channels, associated with cohesive sediments, butsupercritical flow (relatively strong inertial forces) andbifurcation; and (3) broken channels, associated with non-cohesive sediments, and consequent hydraulic jump forma-tion (oscillation around critical flow).[23] Persistent branching channels (illustrated in Delta9 in

Figure 3 (left)) are the focus of this paper and are bestillustrated in the lowest Froude number experiments (Agg1and Agg2, Table 1). Proximal-medial (i.e., mature) channelpatterns are primarily the result of avulsion, a gravitationalinstability, and therefore subcritical Froude numbers onrelatively low gradients (Fr < 0.6 in the experiments). Mostnatural, input-dominated deltas are characterized by thischannel pattern. In these deltas, bifurcation, the gravitation-al deflection of an inertial flow, is restricted to distal regionsnear the shoreline where gradients following avulsion are

Figure 2. Experimental delta sediment mixture; cumula-tive grain size distributions for major grain size compo-nents. A typical mixture (e.g., Agg2) comprises 50 lb G800ceramic microspheres (3M), 25 lb #3 blasting sand, 25 lb #5blasting sand, 2.5 quarts bentonite (Aquagel), 2.5 quarts finekitty litter (Better Way, flushable), 10 lb #12 glass spheres,and 80 g Newdrill Plus polymer (Baker-Hughes). Themixture creates channels without kitty litter but thiscomponent creates roughness on the fluvial surface thatenhances channel formation. This roughness may beanalogous to vegetation in real deltas.


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steeper and channels are shallower and more depositional.This interpretation is supported by the presence of bedforms on mouth bars typically associated with near-criticalflow (small antidunes on mouth bars, e.g., Fr > 0.7[Chanson, 2000]). This indicates that Froude ratio is typi-cally highest near the shoreline, and gradually decreases inan upstream direction (i.e., proximally).[24] Persistent radiating channels (Figure 3 (right)) are

dominated by bifurcation and large wetted areas associatedwith weaker cohesion or high sediment loads. Channels aregenerally straight, and radiate from the fixed inlet becauseof supercritical flow (1.3 < Fr < 2.6). This channel patterndeveloped in both low concentration, relatively weaklycohesive experiments (polymer but no clay; Delta 14 andDelta15), and higher concentration, strongly cohesive sed-iment mixtures (Delta7 and Delta8). In effect, these bifur-cation dominant deltas remain immature; they essentiallyremain in the late inertial bar stage of bar development(discussed in more detail in section 4.3). These deltas aregeometrically simpler, with relatively smooth coastlines andsimpler stratigraphy than their lower Froude number cous-ins. An important aspect of higher Froude number systemsis that upstream information propagation is inhibited. Thishas important implications for delta surface processes andstratigraphy, as much of the delta is effectively out ofcommunication with the shoreline. There is no obvious,natural-scale analog for this channel pattern.[25] The broken channel pattern is also associated with

supercritical flow, but noncohesive sediments. As describedby Sheets et al. [2002], the natural analogs for this patternare most likely steep alluvial fans and fan deltas wherechannel segments are generally very short in comparison todistance to the coast or fan terminus. An interesting differ-ence between the two supercritical channel patterns is theirability to modulate Froude number. Froude numbermeasurements indicate that, in the noncohesive case, hy-draulic jump and cyclic step formation [e.g., Sun and

Parker, 2005], lead to oscillation around critical flow. Flowacceleration leads to supercritical values, and jumps returnthe flow to subcritical conditions. In contrast, the cohesiveexperiments seem unable to ‘‘break’’ channelization with ahydraulic jump, and tend toward very high Froude numbers(Fr for Delta7 is 2.6). Channel patterns associated withsupercritical flow may be more common in deep waterdistributary systems where Froude numbers are generallyhigher than in shallow water systems [e.g., Pirmez andImran, 2003; Normark, 1970].[26] Like channel patterns, mouth bar stacking patterns

are also a function of both Froude ratio and cohesivenessbecause they respond to, and influence, the mechanisms ofchannel migration. In strongly cohesive deltas, bars gener-ally extend and widen symmetrically (Figure 4 (left)). Innoncohesive systems, bank erosion tends to be asymmetric,and widening may occur to one side, resulting in a lateraloffset stacking pattern (Figure 4 (right)). Froude numberalso influences these mouth bar patterns. In high Froudenumber cases (e.g., Figure 4 (left)) the tendency to back upthrough progressive upstream accretion is reduced, makingthe system more likely to move laterally at the bar scale.Such systems only move backward once a significantthickness of sediment has built up through deposition ofmultiple bars. In summary, strong cohesion (and lowerFroude numbers) leads to strong back-stepping at the barscale, while weaker cohesion (and higher Froude numbers)leads to laterally shifting strata at the bar scale.

3.2. Cohesive Experiments (Agg1 and Agg2)

[27] The forgoing analysis of channel splitting mecha-nisms and associated channel patterns suggests that branch-ing channels (Agg1 and Agg2) are the best analogs fornatural birds foot deltas. Exaggerated cohesion and low-sediment concentration promotes strong flow channeliza-tion, low Froude number and the most complex channelpatterns. One measure of the degree of channelization and

Figure 3. Overhead images indicating how delta-channel patterns change as a function of sedimentconcentration. All three experiments were run with the same water discharge and sediment mixture. (left)Delta9 has the lowest sediment concentration (C0), lowest normalized wetted width (i.e., ratio of activeflow width to delta width at half the distance down delta), and lowest Froude number. The channelpattern is dominated by branching caused by avulsion; bifurcation occurs only in the most distal channelreaches. (right) Delta7 has a larger sediment concentration, larger normalized wetted width, shallowerflow, and substantially higher Froude number. This channel pattern is bifurcation dominant, radiatingfrom the fixed inlet. A comparison between the shorelines of Delta9 and Delta7 indicates that avulsiondominated systems have a more complex, rugose coastline than bifurcation-dominated systems. (middle)The Delta8 channel pattern is intermediate between bifurcation dominant and avulsion/bifurcationdominant.


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flow localization is the fraction of subaerial delta surfacearea occupied by flow at any given time. In these experi-ments, the wetted fraction is typically substantially smallerthan observed in the less cohesive experiments (0.05–0.2versus 0.2–0.4 as given by Sheets et al. [2002]) and iscloser to wetted fractions we have estimated from satellitephotos in the modern Mississippi delta (i.e., up to �0.1 onthe distributary lobes and much less on the delta plain).[28] The cohesive experimental deltas typically exhibit 3

or more orders of channel branching with a broad range oflength scales (e.g., channel lengths, widths and depths). Wenote here that the channel cross-sectional aspect ratios(width:depth) observed in the experiments are far smallerthan those observed in natural systems (1–2 in the stronglycohesive experiments, versus 100 for typical natural chan-nels, see Table 1). We would argue, however, that compa-rable Froude ratios lead to more natural development of thelandscape, as indicated in the channel patterns and evolutionof the distributary channel system. We note that the lowestcalculated Froude number (0.21) and lowest aspect ratiochannels are associated with Agg2, the most cohesiveexperiment. This increased cohesion is the result of a longerset-up time. Although Agg2 had the same sediment mixtureas Agg1 and Delta9, (Fr, 0.59 and 0.61 respectively), it wasrun intermittently over 2 months to facilitate topographicscanning. In contrast Agg1, Delta 9 and the other experi-ments were run continuously over a few days and as a resultwere less cohesive.3.2.1. Statistical Analysis of the Shoreline(Cohesive Experiments Agg1 and Agg2)[29] One way to quantify fundamental length scales in the

experimental deltas is to analyze the evolution of theirshorelines (Figure 5). This analysis shows that the increasein the mean distance from the inlet to shoreline (dashed line)is increasing at a gradually diminishing rate. This increase isa consequence of the constant sediment discharge and waterdepth in a radial expanding system. Note that compactionproduces dips in this trend around 60 and 100 h, during longpauses in the experiment.[30] The plot of maximum distance from the inlet to the

shoreline, however, increases in discrete events (solid blackline in Figure 5) leading to roughening of the shoreline as

indicated by shoreline standard deviation, s, in Figure 5. Asis the case in the mean distance measurement, dewateringleads to pronounced dips in this trend (gray portion of thetrace in Figure 5). Major progradation generally occurs attimes immediately following the development of a relativelysymmetrical map pattern, as indicated by relatively lowvalues of shoreline standard deviation immediately preced-ing jumps in maximum distance to the shoreline. Thesemajor progradation events are associated with channelentrenchment and a collapse of the distributary system toa single channel, as indicated by the anticorrelation betweenshoreline standard deviation and wetted area (Figure 6).These large shoreline excursions (ca. 5, 30 and 120 h) canbe considered as an oscillation around grade, a complexresponse to a gravitational instability associated with chan-nel overextension.[31] The steps observed in the maximum distance to

shoreline plot define important time and length scales inthis distributary system. The time between these individualevents increases as the experiment progresses, becauseincreasing amounts of sedimentation and time are necessaryto approach symmetry. However, the major shoreline excur-sions are all of similar length, constrained by the degree towhich the system can extend before becoming inefficient.These length scales represent the largest extension eventsand are diminished by subsequent channel splitting. Chan-nel splitting within a lobe is most frequent just prior toavulsion, when the channel pattern is strongly influenced bydepositional topography. As a result, only the largest eventsare revealed in the shoreline statistics (e.g., Figure 5). Forexample, the greatest contribution of inertially depositedbars to signal (i.e., mean shoreline position) as opposed tonoise occurs when all the flow is contained in a singlechannel soon after a major avulsion event.3.2.2. Surface Observations: Avulsion Cyclefor Cohesive Experimental Deltas[32] The cyclic shoreline behavior observed in the pre-

ceding analysis can be explained by characteristic autogeniccycles that provide a context for all the surface dynamicsand stratigraphic packaging. A specific example from theAgg2 experiment aptly illustrates a characteristic experi-mental avulsion cycle from the topography and isopach

Figure 4. Schematic of bar stacking patterns in experimental deltas made from cohesive (Delta 9) andnoncohesive (Delta 15) sediments. Backstepping bar patterns dominate in cohesive substrates and atlower Froude numbers, while sidestepping (compensational stacking) dominates in noncohesive deltas athigher Froude numbers. Cohesive systems tend to backstep at the bar scale then sidestep at the lobe scale.Noncohesive deltas tend to sidestep at the bar scale and then back up and sidestep.


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maps in Figure 7. Following avulsion, an incisional channelforms and extends across the delta top. Incisional channelformation is most rapid immediately following avulsion asthe relatively steep gradient induces strong erosion and thehighest flux at any stage of the cycle. A jet forms at thecoastline, and the channel extends further via deposition andprogradation (112–114 h), a constructional channel exten-sion process.[33] The flow field images indicate a gradual loss of flow

confinement following initial channel incision and exten-sion (114–120 h). The mouth bar underlying the channelwidens during this period as the flow is lifted and increas-ingly affected by topography (116–118 h). Isopach maps(Figure 7) highlight the gradual shift of deposition to the barmargins as the flow is lifted and forced to spread during bargrowth. The increasing influence of topography leads tobackpressure on the flow, which, in turn, leads to bedaggradation and upstream overbank flow (120 h), a processwe have termed morphodynamic backwater and will discussin more detail. As overbank flow increases, the delta surfaceis ‘‘tested’’ by thin flows and rivulets that form on steeper

Figure 5. Measurements of shoreline dynamics during the Agg2 experiment. Maximum shoreline iscalculated as the maximum distance between the inlet and any point along the shoreline. Mean shorelineis the radius of a semicircle with the same map view area as the subaerial experimental delta. Standarddeviation (s) of the shoreline is the expected distance a randomly chosen point on the shoreline falls withrespect to the mean radius. Gray area on the shoreline plot represents a major episode of delta extensionwhich is keyed to gray area on the time series plot, indicating sudden extension in maximum coastlineposition and increase inshoreline standard deviation.

Figure 6. Time series plot of the number of wet (pink dye)delta top pixels and shoreline standard deviation (alsoillustrated in Figure 5) indicates that these data areanticorrelated. Large shoreline excursions occur when thechannel system incises and collapses to a single channel.


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Figure 7. Flow patterns, topographic scans, and isopach maps on 2 h intervals over an 8 h period duringthe Agg2 experiment. Note initial channel extension (112–114 h), subsequent flow bifurcation (116–118 h), and occurrence of overbank flow and deposition late in the avulsion cycle (120 h). Jet (inertial)and lobe length scales are annotated. Contour marked on images is 1 cm above the flat plate.

Figure 8. Sequential overhead images illustrating overbank flooding associated with the growth of alarge lobe during the Agg2 experiment. Runtimes indicated in upper left of each photo. The maximumupstream extent of overbank flow is marked with a green dot. Ultimate backflooding is observed all theway to the fixed inlet, 1.8 m upstream and approximately 5 cm above base level. Average postavulsionchannel slope is approximately 1:200. Estimated hydraulic backwater length (discussed in text) is shownin Figure 8e for comparison. Stratigraphic section positions for Figure 9 indicated by dashed black linesin Figure 8f.


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gradients and tend to develop into incipient channels, a sortof ‘‘finding phase,’’ separate from the ‘‘entrenched phase’’earlier in the cycle. Since there will be no avulsion without afavorable potential energy gradient, rapid bed and leveeaggradation associated with channel backflooding may be atrigger for avulsion of the flow from the now superelevatedchannel. As a result, avulsion is strongly influenced by barand lobe growth downstream (downstream control).[34] Lower-order, lobe scale flow patterns can be com-

plex and may affect flow over the entire delta. Figure 8demonstrates an upstream migrating wave of overbankflooding or morphodynamic backwater associated with thegrowth of a large downstream lobe in the Agg2 experiment.These morphodynamic backwater events do not propagateupstream monotonically. While the overall progression isupstream, there is at least one period during which thesystem steps toward the shoreline as a new inertial bar isformed (Figure 8c) before continuing back toward the inlet.Figure 9 shows upstream migration of channel bed sedimen-tation as the morphodynamic backwater effect progresses.[35] Upstream controlled channel avulsion is relatively

rare in the experiments, presumably because of the effec-tiveness of downstream control. It was observed in extremecases when channels prograded to the edge of the experi-mental plate (i.e., into deep water), effectively removing anydownstream control. This represented a pure example ofupstream controlled avulsion, as channel superelevation wasdue only to local gradual aggradation in the absence of anydownstream effects. Experimental upstream avulsionsoccurred on much longer time scales than those associatedwith downstream effects. An incidental observation relatingto channel filling is that, in most cases, a channel abandonedby upstream avulsion was left empty, unlike most backfilledchannels which leave very little topographic evidence on thedelta top. It was observed that the gravity-driven process ofadvective flow down levees dominated levee growth. The

rate and height of levee growth was strongly dependent onthe specifics of the grain size distribution, particularly in thesilt size range. Apparently these particles were just sus-pended in channelized flow, but were deposited rapidly inoverbank flow.[36] The experiments indicate that distributary systems

like deltas may be more erosive than is currently thought,with cutting localized in time and space to very specificparts of the avulsion cycle. The degree of erosion dependson the order of the channel that avulses. Erosion occursimmediately following avulsion as the channel extends(incisional channel extension) and, as a result, much ofthe material in incipient mouth bars early in the lobe cycle iserosionally sourced from the delta top (e.g., Figure 7). Later,as the deposit grows, channel erosion decreases and thematerial deposited at the edges of the growing mouth bar ismore likely to be externally sourced from the fluvial systemupstream of the delta. Another phase of erosion is associ-ated with more mature phases of delta growth, as lower-order streams associated with the developing fluvial system(coastal plain) build out over the underlying delta, causingthe entire system to prograde (e.g., Figures 1 and 3 (left)).3.2.3. Subsurface Observations/Stratigraphy(Agg1/Agg2)[37] The experimental stratigraphy can be subdivided into

two general parts, an upper fluvial fan stratigraphy domi-nated by channel surfaces and fills as well as overbanksedimentation, and a lower, submarine portion of clinoformstrata and marine mud (see delta cross sections in Figure 10).Favorable comparisons of the experimental stratigraphywith seismic data from natural deltas give us someconfidence that the cohesive experiments generate realisticgeometries. In particular, the mouth bar geometry and‘‘double downlap’’ growth patterns (Figure 10) are qual-itatively similar to those observed in seismic interpreta-tions of natural deltas [McKeown et al., 2004].

Figure 9. Stratigraphic cross sections along (A-A0) and perpendicular to (B-B0) a distributary channel inthe Agg 2 experiment (sections are shown at different scales). Topographic scan times (indicated inlegend) correspond to those in Figures 7 and 10. Intersection of A and B cross sections indicated bydashed black lines. Plan view positions of these cross sections are indicated by black dashed lines inFigure 8f. Note the low-angle upstream accretion in the cross section A associated with morphodynamicbackwater effects. Further, the cross section B indicates that channel bed and levee aggradation areroughly contemporaneous up to the point when a new channel is formed.


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[38] The 2.5 cm wide thin-sectioned cores of the strata(Figure 11) document a bimodality of laminae thicknessshowing thin-bedded subaerial laminae deposited atopthick-bedded laminae from submarine portions of the delta.The cores also show several important delta facies in theexperimental deposits including: (1) coarse bed load depos-

its/lags at the base of a persistent distributary channel (topcore 1, mantling an erosional surface cut into distributarymouth bar facies); (2) thinly bedded, fine-grained overbank/levee sediments overlying distributary mouth bar deposits(top cores 2 and 3); and (3) fining upward sedimentationassociated with bar deposition during avulsion cycles (bot-

Figure 10. Strike-oriented stratigraphic sections from the Agg2 delta reconstructed from topographicscans. Positions of sections are indicated in Figure 1. Labels 1, 2, and 3 indicate Figure 11 thin sectionlocations. Light gray and dark gray shading indicate weak and strong morphodynamic stages of bargrowth, respectively.

Figure 11. Thin sections (30 mm wide slabs) taken from sediment cores of the Agg1 experiment.Analogous stratigraphic positions are indicated in Figure 10. Section 1 shows proximal bar depositionfollowed by thick channel ‘‘lag’’ coarse-grained deposits. Section 2 shows proximal bar deposits toppedby continuous overbank/levee deposits. Section 3 shows at least two bar packages overlying andseparated by prodelta mud. Fining upward packages are indicated by open triangles and majorstratigraphic boundaries by black lines. Note missing portion of section 2.


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tom cores 1–3, and repeated twice in core 3, indicated byopen triangles).

4. Discussion

4.1. Fundamental Autogenic Cycles

[39] Experimental observations presented in the foregoingsections suggest three fundamental nested autogenic cyclescontrolling river-dominated delta evolution.[40] 1. The inertial bar cycle is the smallest of these, and

is associated with an inertial jet instability at the channelmouth [Syvitski et al., 1998]. A bar cycle involves prograda-tional channel extension from the shoreline, aggradationalmouth bar growth and widening and ultimately channelbifurcation [e.g., Edmonds and Slingerland, 2007], at whichpoint this cycle may begin again.[41] 2. The avulsion (lobe) cycle operates at a larger scale,

and is associated with gravitational channel instability(avulsion). An avulsion cycle is characterized by initialincisional channel extension followed by the developmentof a network of channels and hierarchically arranged barsassociated with avulsion and bifurcation. The terminalelements of lobes are composite mouth bars deposited bythe inertial bar cycle. Lobes are usually hierarchicallyarranged into larger lobes that are associated with avulsionon different orders of the distributary channel network.[42] 3. The delta cycle (inferred but not observed in the

experiments) is the smallest scale over which the delta is onaverage progradational, requiring delta extension over dis-tances significantly longer than the lobe scale. A delta cyclecontains all of the hierarchical, higher-order elements andcycles listed above in a nested fashion, i.e., 1 inside 2,inside 3. In the following discussion we present our inter-pretation for the mechanics of these autogenic cycles andtheir relation to the preserved stratigraphy.

4.2. Positive Feedback, Fundamental Length Scales,and Landscape Inertia: A Source of Landscape ‘‘Noise’’

[43] Perhaps the most striking behavior associated withthe exaggerated cohesiveness in the experimental deltas islow channel mobility. Relatively stable channels lead to atype of ‘‘landscape inertia,’’ whereby the system tends toextend or prograde in a single direction for a prolongedperiod of time, locally overshooting the long-term equilib-rium deposit trajectory (grade), and creating irregularity inthe deposit coastline (e.g., Figures 5 and 6). Such behaviorcontrasts with a system of highly mobile channels wheresedimentation is quasi-diffusive, and the deposit planformapproaches an ideal semicircular coastline. Here channelsrapidly adjust to the path of steepest descent, creating lessnoise in the shoreline shape. The degree to which landscapeinertia affects channel patterns may be related to the flowmomentum, resulting in turbulent jets, or to landforms, suchas subaerial or subaqueous levees, that confine the flow to aparticular course. Evidence for landscape inertia in naturaldeltas like the Holocene Mississippi is the strongly irregularplanform and channel gradients that are well below those atwhich avulsion is theoretically predicted [Aslan et al.,2005].[44] Early stages of the delta experiments revealed that

Froude supercritical flow in the inlet slot generally wentthrough a hydraulic jump to Froude subcritical conditions

prior to exiting the channel and becoming unconfined. Thedensimetric Froude number (Fr0), however, is likely to besupercritical immediately downstream of the inlet, as bydefinition g0 in equation (2) is vanishingly small in homo-pycnal systems like the experiments. In natural systems thissituation will occur when the flow from the channel hasmoved sufficiently far offshore to become fully submergedso that the ambient water depth is substantially larger thanthe channel depth (at least twofold) [Bates, 1953; Ramsayer,1974]. A sudden decrease in the gravity force at the channelmouth leads to excess inertia and rapid mixing with theambient water in the form of an inertial, turbulent jet.[45] The jet region is characterized by rapid flow decel-

eration, perturbing sediment transport at the coast andcausing a strong downstream limit on the extension lengthof channels [e.g., Bates, 1953]. Once a channel reaches thecoast it must fill vertical space in order to be lifted back tothe elevation of the fluvial surface before it can propagateefficiently. Inertial behavior on floodplains has been de-scribed as the progradational phase of alluvial channelextension [Slingerland and Smith, 2004], or the aggrada-tional channel extension phase of Mohrig et al. [2000].[46] The inertial (bar) length scale (‘‘inertial bar scale’’ in

Figure 7) is constrained by channel width, the local dis-charge at a channel mouth and sediment size [e.g., Shieh etal., 2001]. It sets a length for individual mouth bars, afundamental building block of delta stratigraphy. The abso-lute limit to this length scale is not well understood, but islonger than simple jet theory would predict and appears tobe governed by water depth, the rate of shoaling due to bedload deposition, the rate of subaqueous levee deposition,and their influence on jet hydraulics [Edmonds and Sling-erland, 2007; Rowland and Dietrich, 2006]. In the experi-ments, inertial regions are often characterized by adverse(i.e., positive) bed slopes because of the dominance ofinertial over gravitational forces.[47] In contrast to bar length scales set by flow inertia the

tendency toward a long-term equilibrium state (grade) setsan upper limit on the lobe length scale (‘‘lobe scale’’ inFigure 7). This limit represents the maximum distance achannel can prograde before its gradient becomes too low toefficiently transport sediment. The deposition rate at theshoreline is typically much higher than at any other pointupstream in the experiments, leading to a shallowing of thechannel profile. In principle, upstream channel aggradationcould keep pace with shoreline deposition, maintaining thechannel profile during progradation, but this is rarely thecase in deltas. An important control on the lobe length scale,therefore, is the degree to which depositional landforms(such as subaerial levees) force channels to maintain aparticular channel course. Mechanisms of subaerial leveedevelopment are well documented by Adams et al. [2004].They include deposition of sediment advected overbank byflow and diffusion in regions of lateral shear adjacent to aflooded channel. The relative impact of each process isdependent on the amount of standing water on the flood-plain.

4.3. Weak and Strong Morphodynamic Interaction

[48] In both experimental fan and delta systems, the onsetof sudden sediment transport inefficiency is related tosupercritical conditions, either by high gradients on the


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delta top (e.g., hydraulic jumps in supercritical fan deltas,Fr > 1 [e.g., Sheets et al., 2002], as discussed earlier) or thepresence of standing water offshore (e.g., in cohesive birdsfoot deltas, Fr0 > 1). As a result spatial and temporaloscillation around critical flow appears to be an importanttheme in the surface dynamics.[49] For example, surface maps of delta evolution

(Figure 7) and time lapse topographic surface cross sections(Figure 10) indicate that vertical bar and lobe growth andwidening represent a transition from inertially dominatedbar deposition to gravitationally influenced flow bifurcationand, ultimately, gravitationally dominated avulsion. Thistransition can be illustrated with reference to energy con-servation through a simplified Bernoulli equation for flowenergy conservation along a streamline

U2chan

2gþ ychan þ zchanð Þ þ pchan

g¼ U2

bar

2gþ ybar þ zbarð Þ þ pbar

g; ð4Þ

where U is flow velocity, g is gravitational acceleration, y isflow thickness, z is bed elevation, p is pressure, and g is thespecific weight of the fluid. All three terms in thisformulation are in units of length (head) and subscriptsrefer to locations either in the channel or on the bar. Thisequation can be simplified, however, as the flows are opento the atmosphere, (i.e., open channel flow) and pbar = pchan.This leaves only the relative velocity and elevation terms(the first two terms on each side of the equation). Whileenergy conservation is a weak assumption in this case,because the early stages of bar growth are dominated byhighly dissipative turbulent jets, experimental observationsuggest that the stages of bar evolution can be understoodheuristically through the terms in equation (4).[50] Bar evolution involves a transition between two

distinct stages. The first is a ‘‘weak’’ morphodynamic stage,in which the velocity (or inertial) term dominates and theeffect of gravity is weak. During this stage, the flow isstrongly inertial and changes in the form of the bar will haverelatively little impact on flow patterns. Deposits associatedwith this stage are elongated in the flow direction and areessentially a passive response to the flow field, predomi-nantly aggradational, generating a cross-stream symmetricprofile (dark gray-shaded strata in Figure 10). A number ofprevious delta studies have focused on this weak morpho-dynamic stage, for example Shieh et al. [2001] and the‘‘inertial stage’’ of Wright [1977].[51] The second phase of bar development is a ‘‘strong’’

morphodynamic stage, in which the gravitational termdominates and flow interacts strongly with the evolvingbed. The inertial flow is gradually lifted up to the fluvialsurface by submarine sedimentation (increase in both y andz), leading to increased influence of the elevation term inequation (4). This involves a transition from jet-like flow toboundary layer flow with suppressed turbulence. A balanceof inertial and gravitational forces leads to bifurcationassociated with a V-shaped subaerial region developed onthe bar surface (the middle ground bar [Edmonds andSlingerland, 2007]). The deposits of this stage are charac-terized by well-developed clinoforms extending outwardfrom the edge of the aggradational core (light gray-shadedstrata in Figure 10) and bidirectional downlap. This strong

morphodynamic stage is similar to the ‘‘friction-dominated’’stage of Wright [1977] and, in fact, the friction effect growssignificantly as the bar shoals. While we acknowledge thatfriction must be important during this stage, it is likely thatthe decrease in Froude number associated with increase inbed elevation drives the majority of flow spreading. Thegeometric evolution from weak to strong morphodynamicshas been quantitatively documented by planview barlength:width ratios by Shieh et al. [2001].[52] This full cycle of weak to strong morphodynamic

evolution is usually observed only in places where theFroude number is initially high and inertia dominatessignificantly over gravity, for example on a delta edge orflooded fan/delta surface [e.g., McKeown et al., 2004]. Incases where the Froude number can evolve very quicklywith small increases in bar height, the inertial stage may bevery short or nonexistent, changing rapidly to the strongmorphodynamic stage. Bar stratigraphy in such cases (e.g.,well-drained alluvial fans or deep water fans) should recordlittle to no aggradational (jet) core, as observed in theexperiments of Sheets et al. [2002]. Rather, the lobes seemto grow in a geometrically self-similar state by a spreadinggravity flow over the convex bar, which resists rechanneli-zation [Sittoni, 2005].

4.4. Negative Feedback: Morphodynamic Backwaterand Channel Backfilling

[53] A general observation of the cohesive ‘‘branching’’deltas is that channel extension and bar deposition lead tomorphodynamic adjustment over a substantial portion of thedelta. This adjustment represents a form of negative feed-back (self-regulation or homeostasis), compensating forextension beyond grade during the avulsion cycle. Bardeposition near the shoreline leads to an upstream migratingflow disturbance, which causes sedimentation to propagateup the channel. This sedimentation, in turn, leads to in-creased overbank flow, rapid bed and channel levee aggra-dation and, ultimately, induces failure of the channel banksat an advantageous point, producing channel avulsion.[54] The morphodynamic backwater effect we propose is

initiated by sedimentation associated with a hydraulicbackwater effect (‘‘backwater deposits’’ [Senturk, 1994;Batuca and Jordaan, 2000]) that occurs as an incipientbar lifts and decelerates channelized flow. This phenomenonhas been modeled in two-dimensional systems, like a singlechannel or a flume, using the shallow water equations[Chang, 1982; Hotchkiss and Parker, 1991]. However, theinfluence of deposition at the channel terminus and associ-ated backwater effects in three-dimensional distributarychannel networks and on channel and lobe evolution ismore complicated.[55] Since the experimental gradients are relatively high

(Table 1), the hydraulic backwater length in these experi-ments is relatively short. The ratio of characteristic exper-imental flow depths of 2–3 cm to experimental channelslopes of 0.02–0.03 would result in experimental backwaterlengths on the order of 1 m using a common approximationfor hydraulic backwater length [e.g., Paola, 2000; G. Parker,One-Dimensional Sediment Transport MorphodynamicsWith Applications to Rivers and Turbidity Currents, internetE-book, 2005, available at http://vtchl.uiuc.edu/people/parkerg/morphodynamics_e-book.htm]. Channel bed sedi-


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mentation precipitated by the hydraulic backwater deceler-ation, however, can propagate upstream rapidly (i.e., back-water deceleration ! deposition ! more proximalbackwater deceleration ! etc.). As a result, the length scaleof the morphodynamic backwater effect can be substantial,considerably longer than the simple hydraulic backwaterlength. For example, in Agg2 (Figure 8) overbank floodingassociated with backwater effects extends all the way to thefixed inlet, approximately 1.8 m from the shoreline, con-siderably longer than the rough 1 m estimate (Figure 8).This suggests the presence of morphodynamic backwaterthrough which bar and lobe formation has a substantialinfluence throughout the experimental delta.[56] While the controls on hydraulic backwater are well

understood and include channel slope, Froude number andflow thickness [Chow, 1959], controls on the morphody-namic backwater length are poorly constrained. Presumably,processes that affect the magnitude, length and migrationspeed of the hydrodynamic wave, as well as the sedimenttransport variables that control the coupling of the morpho-dynamic wave, are important. For example, variables thatcontrol the channel bed aggradation rate, like the proportionof bed load versus suspended load, may affect morphody-namic coupling. Three-dimensional observations of theexperiment suggest that the upstream limit to the morpho-dynamic length is geometrically constrained. Channels aretypically backfilled to some point at which another, moregeometrically advantageous channel path presents itself(e.g., a steeper path to shoreline).[57] The most important implication of a limit on the

morphodynamic backwater length is that there is someportion of the system above which deposition and channeldynamics operate in the absence of influence from theshoreline. One might expect the morphodynamic backwaterlength to be limited by channel gradient in the distributarysystem itself. In particular, as slope often increases non-linearly from coastline to coastal plain, there might be alimit associated with increasing proximal flow velocities.Circumstantial evidence for this is the tendency for ‘‘nodal’’avulsion styles in many sedimentary systems [Slingerlandand Smith, 2004], where multiple avulsions occur from thesame nodal point.[58] The strength of morphodynamic backwater in the

experiments varies with Froude number as predicted bybackwater theory [Chow, 1959]. They were strongest in thecohesive, low Froude number experiments (e.g., Delta9,Agg1, Agg2), where flow backflooding was typically strongafter the development of a single inertial bar (Figure 4). Inthe more bifurcation-dominated deltas (e.g., Delta7, Delta14,Delta15) backflooding usually occurred after a greater accu-mulation of bars. It is interesting to note that backfloodingis still prevalent in noncohesive, supercritical experiments[Sheets et al. 2007; Sittoni, 2005; W. E. Weaver, unpublishedPh.D. dissertation, 1984]. Here the mechanics of backflood-ing must be somewhat different, as the hydraulic backwaterlength in supercritical flows is extremely short. Rather,upstream migrating deposition appears to be associated withhydraulic jumps.[59] The persistence of morphodynamic backwater effects

in the experiments suggests that feedback in distributarychannel systems may be far more important to geomorphol-ogy and stratigraphy than is currently thought. Channel

filling strata are often explained as a consequence ofpostavulsion waning flow, and internal storeys as a conse-quence of reoccupation of abandoned channels [Mohrig etal., 2000; Slingerland and Smith, 2004]. The presence ofmorphodynamic backwater, however, implies that the inter-nal architecture of many channel fills, at least in deltaicdeposits, might reflect downstream avulsion cycle events,and may be more predictable than previously thought. Forexample, a major trunk distributary channel might record ahierarchical arrangement of storeys associated with repeatedavulsion cycles in more distal, higher-order channels. Thesestoreys might record both erosion and deposition as thegradient of the system evolves during an avulsion cycle.[60] The experimental results may also have important

implications for quantitatively analyzing and modelingbifurcation processes in distributary channel systems. Anal-yses of the stability of adjacent bifurcates [e.g., Slingerlandand Smith, 1998; Bolla-Pittaluga et al., 2003; Federici andPaola, 2003] do not generally include feedback in thedistributary channel network through more than two bifur-cates. The observation that morphodynamic backwatereffects can propagate long distances implies that distributarychannel networks need to be analyzed over much largerregions, and over more nodes, as has been done in solvinghydrological problems in tributary river networks [e.g.,Saco and Kumar, 2002].

4.5. Avulsion: A Gravitational Instability

[61] The final phase in each of the various cycles dis-cussed here, bar, avulsion, and delta scale, is abandonmentof that particular portion of the delta. This can occurintrinsically, as part of deltaic autocyclicity (‘‘downstream’’control) or via abandonment of an entire region due to‘‘upstream’’ controlled channel avulsion. Downstream con-trolled abandonments fall into two categories, bifurcationaround emergent topography during the bar cycle (discussedearlier) and channel avulsion resulting from the morphody-namic backwater effect.[62] The basic requirement for successful channel avul-

sion is that there exists a sufficient potential energy gradientat the point of avulsion such that an incipient channel canrapidly extend and become the preferred course. In the caseof upstream controlled avulsion, the source of the favorablegradient is typically gradual channel bed and levee super-elevation above the floodplain caused by local aggradation.Upstream controlled avulsion may be common in environ-ments where downstream influences are negligible, such asfluvial systems in continental interiors or in deltas where theoffshore conditions create an effective sediment sink. Onemight expect, however, that downstream effects must be-come important as rivers approach the shoreline, particularlyif the offshore bathymetry is shallow. One caveat is that thepresence of backwater itself is not a sufficient condition todrive backwater avulsions. This effect must exceed theinfluence of local aggradation, something which will be verydifficult to evaluate in many cases.[63] In backwater mediated avulsions the development of

a significant potential energy gradient is primarily associatedwith the morphodynamic wave of deposition, which leads toincreased channel bed and overbank sedimentation, as wellas increased overbank flow. This is particularly evident in theoverhead images of channel and overbank flow (Figure 8)


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and down and across channel cross sections presented inFigure 9. The time lapse overhead images show increasingoverbank flow as far upstream as the inlet toward the end ofthe avulsion cycle. The down channel topographic crosssections show gradual upstream accretion of channel fillstrata with time. The channel cross sections show channelbed and levee aggradation at times corresponding toincreased overbank flow. Ultimately a favorable gradientis developed that captures flow, and the avulsion cyclebegins again.[64] A final thought on avulsion relates to the observation

that avulsion cycle dynamics involve a transition from aninertial instability associated with a channel mouth jet(progradational extension) to a gravitational instabilityassociated with channel extension (incisional extension).Unsuccessful (‘‘failed’’) avulsions may be associated withinertial flow downstream of a channel breach that locallyevolves through multiple bar cycles, but because of a lackof favorable gradient is unable to reach the thresholdconditions for the onset of gravitational channel extension.The result of this is a local crevasse splay deposit, animportant component of natural deltaic stratigraphy.

4.6. Delta Processes, Fractals, and Distance Fromthe Shoreline

[65] A number of researchers have documented the fractalnature of tributary systems generally attributed to multiplescales (orders) of erosional bifurcation [Rodriguez-Iturbeand Rinaldo, 1997]. However, the existence of the partic-ular cyclic mechanisms and fundamental scales presentedin this discussion suggests that delta distributary channelnetworks are not fractal. They can be expected to beorganized differently at different distances from the shore-line and with removal from shoreline-related phenomenalike morphodynamic backwater [Morisawa, 1985; Syvitskiet al., 2005; Jerolmack and Swenson, 2007]. Consequentlyon some small deltas channel patterns are dominated bybifurcation (i.e., fossilized mouth bar patterns) [Edmondsand Slingerland, 2007]. At the other end of the spectrum liepurely alluvial dynamics where lower-order channels aregenerally split by upstream-mediated avulsion [Mohrig etal., 2000]. For example, on the Mississippi delta plain,bayhead deltas are dominated by bifurcation (e.g., WaxLake bayhead delta) while larger-scale splitting (e.g., theAtchafalaya River) is dominated by upstream avulsion[Roberts, 1997].[66] The range of channel characteristics in proportion to

distance from the shoreline can be thought of as reflectingchannel maturation. That is, young channel geometries aredominated by their initiation (genetic) mechanism, whereasmature channels evolve to efficiently deliver sediment andwater to the delta front. Distal reaches of the experimentalchannels are wide and shallow, reflecting their juvenilestatus and origin via depositional jets. More proximal andmature channel reaches have generally lower cross-sectionalaspect ratios, tend to be more deeply incised into olderstrata, and are the domain of gravity flows, frictionallydominated boundary layer flows with well-developed andcoarse traction deposits. This change in channel crosssection and mechanics associated with delta maturationcan be observed in any river-dominated delta, for example,the Mississippi delta, as one traverses up river from a distal

to a proximal position along the channel network. It mayexplain, for example, why meanders never occur in thedistal delta distributaries.[67] A transition from downstream dominant to upstream

dominant avulsion processes may represent a fundamentaldifference between deltaic and alluvial systems. Sincesedimentary systems tend to decrease in slope (and Froudenumber) as time progresses, channel patterns may alsoimply evolutionary stages of landscape evolution (i.e.,maturity or time since deposition). For instance immaturelandscapes may be associated with Froude supercriticalconditions (e.g., alluvial fans or delta termini) while fluvialsystems may tend to greater landscape maturity (i.e., lowerslope and Fr).[68] In summary we note that deltas generally evolve

from inertial to gravitational dominated dynamics and fromdownstream to upstream-mediated channel splitting mech-anisms. Channel and channel network patterns evolveappreciably during avulsion cycles, as slope is graduallymodified via sedimentation and abruptly changed via avul-sion. This slope evolution may exert an important control onsmaller-scale structures like bed forms, channel and barpatterns that develop at various times and locations duringan avulsion cycle. Indeed, friction associated with thesestructures and their dependence on gradient and Froudenumber, adds another source of feedback to avulsion cyclesthat is not present in the cohesive experimental deltas.

4.7. Stratigraphy in the Context of the AutogenicCycles

[69] The observation that surface processes can be under-stood through the characterization of a series of nestedcycles implies that deltaic stratigraphy should reflect this.In particular, we should be able to identify characteristicvertical and lateral stacking patterns and grainsize trendsassociated with bar, avulsion and delta cycles. The bar cyclegenerally involves a transition from weak to strong mor-phodynamics, as does the avulsion cycle, with its earlystages comprising one or more bar cycles and later stagesassociated with strong morphodynamic backwater effects.This transition from inertial to gravitational flow is associ-ated with a general loss in flow competence as frictionincreases and flow becomes increasingly unconfined. Onemight expect this loss in flow competence, in turn, to lead toincreasingly proximal deposition of coarser-grained sedi-ment load and a general fining upward of the deposits at aparticular location. Though the general loss in flow compe-tence records an overall cyclic transition from positive tonegative feedback, the stratigraphic details will be a conse-quence of nested cycles at multiple scales. For example, asis shown in Figure 8, morphodynamic backwater recedesslowly upstream in response to lobe growth but will alsointermittently reverse this overall tend as smaller channelsextend, erode and then backfill.[70] Bar cycle stratigraphy is relatively straightforward to

interpret. The lowest portions of the cores shown in Figure 11show key aspects of characteristic bar cycle stratigraphy.These packages generally fine upward, but comprise sedi-mentation from both the positive and negative feedbackstages of the bar cycle. Passive settling during the inertialstage is recorded by a uniform grain size lower bar in core 1(indicated by white bar). This uniform grain size succession


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is absent in the other cores because of missing material(core 2) or a more lateral position (core 3). The negativefeedback stage of the bar cycle is recorded as a finingupward cap above the uniform grain size base present in allthree cores. This pattern is repeated twice in core 3, wherethe lower bar sequence did not build all the way to the watersurface and therefore there was additional room for asecond, thinner bar sequence. The upper bar sequence incore 3 shows more rapid fining because of deposition inshallower water, and therefore more rapid morphodynamicevolution. Because of the relatively small aerial influence ofthe bar cycle, it is likely that very little of the stratigraphyhigher up in the cores is related to individual bars.[71] Multiple avulsion cycle patterns are recorded in all

three cores, though they are more difficult to discern. Core 1shows a partial bar succession followed by an erosionallybased, coarse-grained, distributary channel filling succes-sion. The bar and some lower portion of the channel fillcorrespond to the first avulsion cycle, though the upperportion of the channel fill must correspond to a series ofsubsequent avulsion cycles that were fed through thisdistributary channel. Cores 2 and 3 show initial avulsioncycles with well-preserved bar sequences at their bases (twobar sequences in core 3). The overbank stratigraphy overlyingthese, however, is more difficult to interpret. The fine-grainedlayering corresponds to increased overbank deposition duringbackwater conditions associated with multiple avulsioncycles, though without chronostratigraphic information wecannot break out individual events. One possible interpreta-tion is given (Figure 11), though each of the individual layersapparent in the upper third of core 3 might correspond to aseparate avulsion cycle.[72] Avulsion and breach of the upstream subaerial levees

usually begins slowly. The trigger is lobe accretion becauseof inefficient overbank flow and the formation of manysmall channels near the end of lobe development (driven bychannel backfilling and morphodynamic backwater). As aresult, a typical (lower-order) lobe at the end of the avulsioncycle is a topographic high containing filled channel depos-its encased in muddy levees. The lobe may have little or nosurficial evidence of the original channel network, just asmooth convex cross section that will deflect subsequentflows (e.g., see the surface of the delta in Figures 1, 3, 7,and 8). Channel fills fine upward and may even end up as amud plugged channel contained in sandy channel fills,because of the slow redirection in water discharge fromthe old lobe to the new channel. This stratigraphy is in turnencased in the fine overbank and levee deposits of thefloodplain.[73] All of the deltaic experiments presented here were

shorter-lived and smaller than we would expect for a full-scale delta cycle at experimental scales. This is indicated bythe fact that morphodynamic backwater effects were able topropagate across the entire delta, from shoreline to inlet,even at the end of the experiment. Delta cycles which areassociated with upstream controlled avulsion, should leavean overall progradational package at a particular location,followed by a major marine flooding surface. The prograda-tional part of the delta cycle is most obvious in core 1 ofFigure 11, where bar deposits are overlain by coarserchannel deposits, and underlain by thin prodelta deposits.

None of the experiments were allowed to run long enough,nor were they large enough, to evolve to the point whereupstream controlled avulsion led to a major abandonment.

4.8. A Depositional (or Conceptual) Modelfor River-Dominated Deltas

[74] The process interpretations presented above providethe basis for a new depositional model for river-dominateddeltas. Overall, deltaic surface processes can be understoodin the context of three nested autogenic cycles [e.g.,Roberts, 1997; Jerolmack and Swenson, 2007]. From small-est to largest these cycles are: (1) the inertial bar cycle,associated with a transition from the dominance of inertialto gravitational forces at the shoreline; (2) the avulsioncycle, associated with gravitational channel extension, for-mation of multiple bars (making a lobe) and, ultimately,morphodynamic backwater and backwater controlled avul-sion (i.e., downstream controlled); and (3) the delta cycle,associated with delta growth integrated over a number ofprograding and aggrading lobes before regional abandon-ment by upstream controlled avulsion processes. Thesenested cycles provide a context for understanding and linkingmany aspects of natural deltaic evolution, including avulsion,channel formation and bifurcation, and the evolution ofmouth bars, lobes and stratigraphy [cf. Roberts, 1997].[75] Further, we propose the following three stages of

deltaic evolution at the lobe (avulsion cycle) scale. Stage 1,positive feedback (channel extension and inertial bar for-mation) involves sheet flow exiting a channel and extendingacross the fluvial surface via incisional channel extension tothe coast, forming a jet where the channelized flowdebouches into standing water. Channel extension proceedsvia a progradational stage, forming a narrow, primarilyaggradational mouth bar that extends basinward under theevolving jet (i.e., weakly morphodynamic bar growth).[76] Stage 2, negative feedback (bar aggradation and

morphodynamic backwater) can be broken into two steps.The first step involves bar aggradation above the pointwhere the incipient topography affects the flow (i.e., stronglymorphodynamic bar growth). Gravitational forces begin torival inertial forces, leading to flow widening and flowbifurcation, leaving a V-shaped subaerial region on the barsurface and ending the bar cycle. At this point, gravitationalforces in a bifurcate channel may overwhelm inertial forcesand the bar cycle repeats. The second step of negativefeedback involves a morphodynamically mediated backwa-ter effect. As the bar grows, a hydraulic backwater effectpropagates slowly upstream, and is immediately followedby a wave of channel bed aggradation. As the lobe con-tinues to grow and channel bed aggradation increases,overbank flow drives accelerated subaerial levee growth.The combined effect of bed aggradation and levee growth issuperelevation of the channel, and ultimately avulsion, dueto gravitational instability.[77] Stage 3, channel avulsion involves the progressive

overbank flooding associated with the upstream migratingmorphodynamic backwater wave, which ultimately leads tothe ‘‘discovery’’ of a more favorable path to the shoreline.While there may be any number of failed avulsions (creat-ing potentially substantial deposits) as flooding progressesupstream, the first path steep enough to promote incisional


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channel extension will be the site from which a newavulsion cycle begins.

5. Conclusions

[78] Progress in experimental morphodynamics has beenhindered by the inability to create realistic experimentalmodels of cohesive, river-dominated (birds foot) deltas withcomplex channel patterns and irregular coastline shapesapproaching natural complexity. The root of this problemis apparently associated with a discrepancy in timescalesbetween the activity of natural cohesion and the rapidmorphodynamic evolution rates in small-scale experiments.In the experiments presented here we address this problemby creating strongly cohesive sediment mixtures usingartificial polymers. The resulting cohesive deltas are Froude(Fr) subcritical and are characterized by well-developedchannelization, low-wetted area, and slow channel migra-tion rates. These new techniques provide the basis forsolving many problems in fluvial and deltaic systems thatwere previously inaccessible to experiment, and allow theformulation of new hypotheses regarding many aspects ofdeltaic behavior.[79] Perhaps most importantly, the experiments allow the

isolation and identification of a series of paired positive andnegative feedback cycles that control deltaic evolutionacross a range of time and length scales. These cyclesrepresent the tendency for deltaic systems to oscillatearound long-term stability because of the presence ofintrinsic instability in morphodynamic systems. While aparticular instability will tend to drive the system away fromequilibrium (e.g., channelization), the nature of morphody-namic systems requires self-regulation (e.g., deposition andlowering of the slope) and a return to quasi-equilibriumconditions.[80] This sort of behavior leads to three important cycles

characteristic of deltaic evolution. The smallest and mostrapid of these is the bar cycle, involving a transition frominertial to gravitational flow and deposition at a channelmouth. At intermediate length and time scales the avulsioncycle dominates, wherein multiple bar cycles may integrateto promote morphodynamic backwater effects that canpropagate upstream over surprisingly long distances. Thelargest scale of evolution is the delta cycle, associated withlong-term behavior of major distributary channels, and,ultimately, upstream controlled avulsion and abandonmentof large regions of the delta.[81] The combination of hydraulic backwater and depo-

sition at the terminus of distributary channels producesmorphodynamic backwater effects that can propagate sig-nificant distances upstream. This effect is particularly pro-nounced in the deltaic environment, because of the nature ofthe subaerial-submarine interaction at the shoreline. How-ever, we also expect morphodynamic backwater effects tobe important in a variety of distributary systems wherechannel fills and upstream accretion have been recognized[e.g., Gardner and Borer, 2000]. It will be advantageous toinclude analysis of possible downstream influence in futuremechanistic studies in these environments.[82] In particular, the pervasiveness of downstream

effects in the experiments suggests that similar phenomenashould be considered as potential influences on channel

(multiple storeys) and overbank (levee and splay distribu-tion) deposition far removed from the shoreline. Further,avulsion dynamics in many regions might be better under-stood as a consequence of downstream control. Whilemorphodynamic backwater effects make deltaic evolutionmore complicated than previously thought, implying link-ages between surface processes in many parts of the delta,the recognition of this phenomenon should allow moresophisticated and accurate models of deltaic behavior.

[83] Acknowledgments. The inception of this industrial physicalmodeling effort was part of the Shapes project (�2000–2005). We wouldlike to thank John Van Wagoner, Shapes team members, and ExxonMobilmanagement for enthusiastically supporting and participating in the devel-opment of a dynamic experimental sedimentology/stratigraphy program atExxonMobil Upstream Research Company. Neal Adair, David Awwiller,Dave Giffin, and John Leiphart are thanked for assisting with variousaspects of the experiments at EMURC. Roger Bloch, John Martin, DougEdmonds, Rudy Slingerland, and Juan Fedele stimulated useful discussionsof delta dynamics. In addition we thank Jana van Alstine for loading theAgg2 data into Petrel, from which the cross sections in Figure 9 weregenerated. The authors are also grateful to Paul Dunn, who carefully andinsightfully reviewed this manuscript and to reviewers David Mohrig,Janok Bhattacharya, and Miles Hayes for useful editorial suggestions.Finally, we would like to thank Chris Paola for the stimulating experimentaland theoretical work at SAFL and specifically for access to the DB-03overhead images.

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Box 357940, Seattle, WA 98195, USA.


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