On the dense bubble clouds and near bottom turbulence in the surf zone

On the dense bubble clouds and near bottom turbulence in the surf

zone

Svein Vagle and Peter ChandlerInstitute of Ocean Sciences, Sidney, British Columbia, Canada

David M. FarmerGraduate School of Oceanography, University of Rhode Island, Kingston, Rhode Island, USA

Received 15 July 2004; revised 11 May 2005; accepted 2 June 2005; published 27 September 2005.

[1] Measurements of high-frequency (100 kHz) acoustical backscatter in the surf zonehave identified the presence of a wall formed by dense assemblages of bubbles generatedby breaking gravity waves and persisting for periods up to 30 min. These bubbles areadvected by alongshore and cross-shore rip currents and are controlled by the localwave field, turbulence, dissolution, and buoyancy. During the summer of 2000 thelocation of the bubble wall south of Scripps Pier, California, was tracked for a 6-weekperiod. Distinct categories of bubble wall defined by the backscatter intensity data areobserved, distinguished by the presence or absence of rip current activity. Theresults suggest that presence or absence of long-period waves (10–20 s) may play a role incontrolling the bubble wall type. During periods without rip currents the location of thebubble wall is controlled by the incoming wave field. Simultaneous turbulencedissipation measurements 0.4 m above the seafloor show clear dependence on the localwater depth beneath incoming waves. The acoustical backscatter data are interpretedusing in situ bubble and turbulence measurements in conjunction with a simple modelbased on bubble sorting by buoyancy, dissolution, and turbulence.

Citation: Vagle, S., P. Chandler, and D. M. Farmer (2005), On the dense bubble clouds and near bottom turbulence in the surf zone,

J. Geophys. Res., 110, C09018, doi:10.1029/2004JC002603.

1. Introduction

[2] Acoustic propagation in the surf zone is associatedwith some of the most difficult and challenging problems inunderwater acoustics. Sloping bathymetry in shallow watercombined with rapidly changing waves and subsequentwave breaking and the generation of turbulence and denseclouds of bubbles all add to the complexity of the use andinterpretation of acoustical signals. Here we report on long-term measurements of the ubiquitous bubble field in a studycarried out near the Scripps Pier and discuss observedvariations in terms of the physical processes of the surfzone.[3] Waves approaching the shore increase in steepness as

the water depth decreases. Recently there has been consid-erable progress toward modeling quantitatively the shoalingwave transformation [e.g., Chen et al., 2000]. When thewave steepness reaches a limiting value, the wave breaks,generating large numbers of bubbles in the water as well asdissipating energy, inducing nearshore currents and forcingan increase in mean water level. The waves will break whenthe local RMS wave height is approximately 0.4 times thelocal water depth [Thornton and Guza, 1983] and the surfzone is the region extending from the seaward boundary of

wave breaking to the limit of wave run-up on the beach. Inthe surf zone wave breaking is the dominant hydrodynamicprocess. There are numerous types of surf zones with a widerange of geometries and bottom topographies but generallythey get shallower toward the beach.[4] The current in the surf zone is composed of motions at

many scales, forced by several processes. There is a quasi-steady current driven by breaking waves, the tide and thewind field, and oscillatory flows due to wind waves andinfragravity waves [Thornton et al., 2000]. Wave and windinduced alongshore currents flow parallel to the shorelineand are strongest in the surf zone, decaying rapidly seawardof the breakers. Studies have found significant tidal signa-ture in the alongshore currents associated with cross-shorechanges in the surf zone width [Thornton and Kim, 1993].Rip currents, which are highly three-dimensional, strong,narrow currents flow seaward from the surf zone. Thesecurrents are fed by alongshore flow in the surf zone andincrease from zero between two neighboring rips, to amaximum just before turning seaward to form the rip. Ripcurrents are common on coastlines and are a dominantmechanism for transporting bubbles and sediments awayfrom the active zone of wave breaking [e.g., Smith andLargier, 1995; Aagaard et al., 1997; Vagle et al., 2001].Very few field measurements of topographically controlledrip currents are available, mainly because of the difficultiesassociated with making suitable observations in rip current

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, C09018, doi:10.1029/2004JC002603, 2005

Copyright 2005 by the American Geophysical Union.0148-0227/05/2004JC002603

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channels, which tend to migrate alongshore. Observationsthat have been presented demonstrate pulsations in the ripcurrents on the wave group timescales (25–250 s) [Aagaardet al., 1997; Brander and Short, 2001]. The hypothesis thatthe observed infragravity frequency pulsations of the ripcurrents are caused by cross-shore standing waves is sup-ported by some recent measurements by MacMahan et al.[2004a]. Energetic very low frequency surf zone eddieshave also been found to influence rip current morphology[MacMahan et al., 2004b], and recent laboratory studieshave also increased our understanding of these phenomena[Kennedy and Thomas, 2004].[5] The density and dynamics of the surf zone bubble

field are governed by a number of physical parametersincluding wave breaking, and the bubbles generated bythe incoming breaking waves dominate acoustical volumescatter in the surf zone. The bubbles entrained by breakingwaves are initially concentrated into plumes, which extendbeneath and behind the wave crests. Shortly after creationthe bubble plume begins to dissipate through buoyancy,dissolution, turbulent diffusion and the more coherentalongshore and cross-shore flows. Large variations in thespatial and temporal distribution of the bubbles occur at thistime. The number density and size distribution of bubbleswill depend on the breaker type, incident wave field,topography, turbulence levels, gas saturation levels, andnearshore currents. Air fractions in newly formed plumescan exceed 50%; with much lower values between theinjections [Deane and Stokes, 1999].[6] In a previous study Farmer et al. [2001] found that

acoustical propagation in the surf zone involves interactionwith both the surface and the seafloor and that the surfaceboundary condition is dominated by the shoreward propa-gation of surface gravity waves. These waves tend to bemuch more coherent and directional than waves in the openocean and their shape and amplitude changes with time in afairly consistent fashion; as they approach and movethrough the breaking zone, the instantaneous water depthcan change by a factor of two or more. Changes in themorphology can also occur over a tidal period because ofsediment transport.[7] During this study spilling breakers, where the wave

crest becomes unstable and cascades down the shorewardface of the wave, dominate. Although almost all wavesbreak by the time they reach shallow water, observationsshow that breaking occasionally occurs several tens ofmeters seaward of this zone. These isolated breaking eventshave significant implications for acoustical propagationsince bubble plumes generated by the breakers may inter-mittently block acoustic signals [Farmer et al., 2001]. Thesebubble clouds, which occur offshore of the main breakingzone, are distinct from the coherent bubble wall wherebubble injections from individual breakers remain sus-pended until the following breaking wave passes, resultingin the presence of dense quasi-stationary bubble clouds. Inthese cases high-frequency (>20 kHz) propagation willremain continuously blocked because small bubbles atten-uate and scatter incoming sound waves efficiently [Smith,1993; Thorpe and Hall, 1993]. Deane [2000] reportedattenuation levels as high as 26 dB m�1 at 10 kHz,effectively blocking most forward propagating signals.The establishment of the bubble wall where the residence

time of a particular plume of bubbles is longer than the timebetween plume injections depends on the location andfrequency of breaking, the saturation levels of the dominantgases (O2 and N2), turbulence levels and nearshore currents.[8] In the present study, carried out with support from the

U.S. Office of Naval Research High Frequency AcousticsProgram, long-term 100 kHz acoustical backscatter mea-surements combined with short-term observations of surfzone bubble size distributions and near bottom turbulenceare used, in combination with a model describing theevolution of the bubble field to characterize the bubble walland its variability, including the effects of rip currents.

2. Observational Approach

[9] In August and September 2000 continuous observa-tions were made of the bubble field in the surf zone next toScripps Pier, La Jolla, California. This experiment was acollaborative effort including researchers from the Instituteof Ocean Sciences, Scripps Institution of Oceanography andWoods Hole Oceanographic Institution. A 100 kHz sidescan transducer was mounted at the end of the pier,approximately 300 m from the beach at high tide (meantide range of 1.5 m), as shown in Figure 1a. The transducerwith beam widths of 1.8� in azimuth and 45� in elevationwas positioned to ensonify channels at an angle of 7�shoreward from the end of the pier, and positioned 4 mfrom the seabed in waters with mean depth of 8 m. Thetransmitted signals were repeat sequence Barker codesoptimized for backscatter Doppler measurements having atotal duration of 16 ms [Pinkel and Smith, 1987; Trevorrowand Farmer, 1999]. The reverberation typically lastedover 20 ms. The sonar was programmed to transmit at2 Hz for an 18 min period every 2 hours. In additionthe sonar continuously recorded 10 s averages of range-gated backscatter throughout the 6-week measurementperiod (14 August to 25 September 2000).[10] During the experiment a time series of 10 s averaged

100 kHz backscatter intensity from the range-gated sonar(Figure 1a) was acquired. Averaged backscatter data fromthis 6-week period as well as significant wave height andwind speed are shown in Figure 2. The backscatter data setis uninterrupted with the exception of a single 84-hour gapfrom 15 to 18 September when the system was down forservicing. The data set spans a period with relatively lowwinds and waves and no major storms. The data shown inFigure 2a have been normalized by the overall mean range-dependent backscatter profile to remove spreading losses inthe wedge-shaped insonified channel.[11] For an intensive 3-day period (25–27 August) an

instrumented frame (Vagle et al. [2001] and Figure 1),courtesy of G. B. Deane (Scripps Institution of Oceanogra-phy), was also deployed in the surf zone 160 m shorewardof the sounder (140 m from the beach at high tide) for in situmeasurements of bubbles, turbulence, and alongshore cur-rents. This frame was equipped with an acoustical resonator[Farmer et al., 1998] for 0.2 s snapshots of bubble sizedistributions, 1.5 m above the seafloor, and a 2 MHz pulse-to-pulse coherent acoustic Doppler sonar (Dopbeam, Son-tek) for measurements of alongshore currents, and turbulentdissipation rates, 0.4 m above the seafloor. The deploymentapproach required that the instrumented frame be partially

C09018 VAGLE ET AL.: DENSE BUBBLE CLOUDS IN THE SURF ZONE

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exposed at low tide and this precluded acquisition ofmeasurements at low tide. A video camera on the pierwas used during daylight hours to aid in the interpretationof the surf frame data.[12] The resonator measured the bubble size distribution

of bubbles with radii between 20 and 600 mm every 0.5 s.The Doppler sonar was mounted with the acoustic beampointing alongshore and perpendicular to the dominantsurface gravity wave direction, thus minimizing the influ-ence of the wave orbital motion on the velocity measure-ments [Veron and Melville, 1999]. This instrumentmeasured velocity fluctuations parallel to the beach at arate of 20 Hz over a 0.72 m path every 0.6 cm starting

0.14 m ahead of the sensor head. The diameter of the sonartransducer is 2.5 cm and the beam spread half angle is 1.1�for a circular piston transducer [Veron and Melville, 1999].Near field effects are limited to the first 0.2 m and themaximum beam spread is 3.5 cm at the far range of theprofile (see Zedel et al. [1996] for details). With thisoperating range the well-known ‘‘range-velocity’’ ambigu-ity [Veron and Melville, 1999] results in direct unambiguousvelocity measurements of ±0.18 m s�1. The measuredvelocity fluctuations were unwrapped using the schemedescribed by He [1997] to extend the velocity measure-ments to values greater than the maximum unambiguousvelocity. This unwrapping scheme assumes that the back-

Figure 1. (a) Plan and (b) cross-shore view of Scripps Pier and instrument layout during theexperiment.


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scatter remains coherent between successive transmissions.For the present analysis the essential step is spatial unwrap-ping, which is inherently a more robust procedure thantemporal unwrapping. Low-pass filtered, to remove high-frequency turbulent fluctuations, path averaged velocityrecords from this sonar gives a measure of alongshorecurrent speeds 0.4 m above the ocean floor. The time- andrange-dependent velocity field fluctuations obtained wereused to estimate energy dissipation e using Kolmogorov’shypothesis.[13] The Kolmogorov model implies an inertial subrange

where the three-dimensional wavenumber spectrum of ahigh Reynolds number flow has a universal form whichonly depends on the energy dissipation. For isotropicturbulence, the one-dimensional wavenumber spectrumS(k) takes the form [Hinze, 1975]:

S kð Þ ¼ A18

55e2=3k�5=3; ð1Þ

where k is the wavenumber and A = 1.5 is an universalconstant. The wavenumber spectrum is calculated for eachvelocity profile using Hilbert spectral analysis [Huang etal., 1998, 1999]. The measured velocity profile represents abroadband signal which is decomposed into several narrow-band intrinsic mode functions. Application of the Hilberttransform on these intrinsic mode functions yields the localwave numbers and amplitudes as a function of profilingrange and the wavenumber spectrum is obtained byintegration of the squared amplitude along the entire profile.The profiling range of 0.72 m and coarsest spatial resolutionof 0.35 cm determine the wavenumber resolution of9 rad m�1 < k < 180 rad m�1. The characteristic timescaleassociated with the inertial subrange t = (n/e)1/2, depends onthe kinematic viscosity n and the dissipation e [Hinze,

1975]. For typical dissipation values encountered in the surfzone, this timescale ranges from O(10�2 s) to O(1 s),therefore velocity spectra have been averaged at 1 sintervals to obtain robust spectra. These spectra arecompared to the inertial subrange slope of k�5/3, whichrepresents an idealized case of isotropic, steady turbulence.For the full range profiles about 70% of the spectra haveproperties consistent with an inertial subrange. For theremainder of the spectra the slope that differed from k�5/3,attributed to lack of isotropy or non steady turbulence. Inthe following only spectra that fit the Kolmogorov modelhave been used.[14] A major challenge of turbulent velocity measure-

ments in the presence of gravity waves is the discriminationof wave induced motion and turbulence. In the present studythe effect of the wave induced motion has been minimizedby carefully aligning the direction of the velocity measure-ments with the direction perpendicular to the direction ofthe incoming waves. The largest scale resolved in ourvelocity profile is k = 9 rad m�1 and therefore the horizontalcomponent of the wave induced motion, u1 = aw/kh isO(10�2). A small component of this motion would benegligible relative to the overall measurements.[15] The seafloor near Scripps Pier is predominantly

composed of coarse sand. Three bottom mounted pressurearrays deployed by G. B. Deane and his group provided2 Hz sampling of the instantaneous sea surface elevationalong two transects parallel to the shore and one roughlyorthogonal to the beach (Figure 1). These data were filteredover the gravity wave spectrum (5–20 s) and processed intotime series of wave heights. Low-pass filtering of the cross-shore array allowed for specification of the beach slopealong most of the distance between the pier mounted sonarand the instrumented frame (Figure 1b). On the basis ofthese observations the beach slope was estimated to be 1:33

Figure 2. (a) Six-week record of 100 kHz sonar backscatter data in dB relative to time-averaged meanand (b) hourly significant wave height and wind speed data. During the crossed period the sonar systemwas down for servicing.


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between the pier-mounted sonar and the instrumented framein the surf zone.[16] The Climate Research Division at SIO collected

wind, wave and water level data, at the seaward end ofScripps Pier, every 5 min. The Coastal Data InformationProgram (CDIP) using a single point pressure sensor atthe end of the pier collected parametric and spectral wavedata. A 2-day gap in the CDIP wave data was filledusing data from the Climate Research Division wavedatabase.

3. Results

[17] Tidally controlled semidiurnal variability of theshoreward extent of the high-backscatter area is expected,and is clearly seen in the data (Figure 2). In addition there ismodulation of the bubble wall location with timescales ofmany days, partly associated with changes in water leveland the incoming wave field. The wave energy as a functionof wave frequency from the CDIP data measured at the endof Scripps Pier is shown in Figure 3. The wave spectra werecalculated on an hourly interval using 34 min of sea surfaceheight data. The wave data reveal typically low-energysummer conditions with the significant wave height exceed-ing 1 m only once during the 6-week period. The frequencydistribution of energy in the wave field exhibits generallybimodal spectra with low-frequency swell (<0.1 Hz) com-bined with periods of higher-frequency waves presumablyassociated with more local weather systems.[18] A more detailed inspection of the backscatter data

also shows significant large-scale differences in the appear-

ance of the backscatter field over periods of hours, andserves to characterize the mobility of the bubble wall. Astationary bubble wall includes those sections where thelocation of well defined regions with high backscatterintensity varies less than 20 m over any given 20-minperiod (an example is shown in Figure 4a.) Eighteen percentof the data show this type of bubble wall.[19] During periods with a mobile bubble wall the well-

defined high-backscatter regions vary in position by morethan 20 m over 20 min (Figure 4b). This type of bubble wallwas observed for 3 of the 6 weeks and is more ambiguous inthat high-intensity backscatter is evident but not organizedas a coherent alongshore feature. Figure 4b shows a 90-minsegment of backscatter intensity from such a mobile bubblewall, with the wall clearly visible as a semicontinuous bandof high intensity located about 120 m from the sonar. Alsoevident is a slanted band of high-intensity backscatter thatshows up for about 15 min starting at 07:55. This featurecorresponds with the occurrence of a rip current [e.g., Smithand Largier, 1995; Vagle et al., 2001]. In this example therip current diffuses and disappears at a distance of about60 m from the sonar, or approximately 240 m from thebeach, and a few minutes later the bubble wall reemerges asthe dominant feature in the backscatter image.[20] An analysis of all the data shows that in the absence

of rip currents the bubble wall spread, defined as thedifference between the most shoreward and most seawardlocation of the bubble wall within a 30-min period isbetween 10 and 40 m for 90% of the data. In the presenceof rip currents the corresponding spread is between 22 and60 m.

Figure 3. Time series of wave energy from CDIP data collected at the end of Scripps Pier. The unevenlydashed horizontal line indicates the presence and absence of mobile bubble wall, and the triangles at thebottom of each panel indicate times when rip currents were observed.


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[21] Approximately 32% of the backscatter data show nodistinct bubble wall. These periods occurred during times ofnegligible wave energy. Figure 5 shows the spread in bubblewall location over 30-min periods for the 6 weeks of theexperiment. The shaded envelope represents the minimumand maximum range of the observed bubble wall within the30-min periods. Observed rip currents are identified withsolid lines. As expected, rip currents are associated withsignificant bubble wall spread. For example, during theperiod from 23 to 26 August the 30-min spread is more than40 m while during the period from 1 to 4 September thecorresponding spread is less than 10 m.[22] The energy dissipation rate, e, from the turbulence

measured with the Dopbeam sonar 0.4 m above the seabedshows significant long- and short-term variability with morethan three orders of magnitude change in the observeddissipation levels from less than 10�7 m2 s�3 to more than10�4 m2 s�3 (Figure 6). Longer-term variability in the waterdepth associated with the local tide will modulate the nearbottom turbulence dissipation levels, with the minimum and

maximum values for e increasing with decreasing waterlevels. In a rip current the overall energy dissipation rateincreases and there is a corresponding decrease in the short-term variability; two such events are identified in Figure 6.The dissipation rate approaches 4 � 10�4 m2 s�3 during themost energetic part of the second event. Overall, the e datashown in Figure 6 approach a log normal distribution.

4. Discussion

[23] Backscatter from sound propagating into a wedge-like sound channel with complicated upper and lowerscattering boundaries makes it difficult to calculate thescattering cross section per unit volume, Mv, from the sonardata.[24] The changing tide and wave field, together with

bathymetry, modify the scattering volume. Simple calcula-tions based on the transmitted pulse length, transducer beamcharacteristics and a bottom slope of 1:33 indicate that thescattering volume reaches a maximum of 16 m3 at adistance of 115 m from the sonar at high tide and approx-imately 8 m3 at a distance of 80 m at low tide. When bubblesize distributions are available from the acoustical resonatoron the instrumented frame it is possible to compare thesewith the 100 kHz backscatter data to assist in the interpre-tation of the sonar signals.[25] The scattering and extinction cross sections per unit

volume, Mv (m�1) and Se (m

�1), can be defined as

Mv ¼Za¼amax

a¼amin

ss a; fð Þn að Þda ð2Þ

and

Se ¼Za¼amax

a¼amin

se a; fð Þn að Þda ð3Þ

where ss(a, f ) and se(a, f ) are the scattering and extinctioncross sections for a bubble of radius a insonified at afrequency f [Urick, 1983] and n(a)da is the number ofbubbles having a radius between a and a + da per unitvolume as obtained from the acoustical resonator. From (3)the frequency-dependent sound attenuation ab in dB m�1

for sound propagating through the bubble wall will be

ab ¼ 4:34� Se ¼ 4:34

Za¼amax

a¼amin

se a; fð Þn að Þda: ð4Þ

The calculated Mv values for a 2-hour period on 27 Augustare shown in Figure 7a. The noise threshold level of thisparticular instrument is approximately Mv = 10�7 m�1. Theend of the record shows instrument saturation due toincreased wave breaking over the instrument caused by anoutgoing tide. Figure 7b shows the corresponding Mv valuesfrom the 100 kHz sonar when the maximum levels over a6-hour period have been scaled by the resonator estimates.Nevertheless, the data show coherence with longer periodvariability in bubble plumes during large breaking events

Figure 4. Classifications of the bubble wall determined bycharacteristics of periods with high backscatter intensityfrom the 100 kHz sonar positioned at the seaward end ofScripps Pier. (a) An example of a stationary bubble wall and(b) an example of a mobile wall with a rip current between07:50 and 08:15.


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and rip current events as the ones indicated by vertical linesin Figure 7. The lack of statistical consistency at lowerbubble concentrations may be due to the fact that theinsonified volumes are not exactly colocated and moreimportantly, the fact that the observed backscatter intensitiesare range integrated values, making them more sensitive tobubbles further seaward. As the bubble wall moves offshorefrom the instrumented frame the observed backscatterintensity decreases at this location because of increased

attenuation further offshore and the difference in observedbackscatter intensity and backscatter intensity inferred fromthe in situ bubble measurements at the location of theinstrumented frame increases. The significant increase inattenuation can be seen in Figure 7c where the attenuation indB m�1 has been calculated using (4) for the bubble sizedistributions used for the calculations shown in Figure 7a.During breaking events in the rip current and after thebubble wall has moved further offshore, the attenuation

Figure 5. Envelope of observed minimum and maximum bubble wall location within 30-min periods,defined as bubble wall spread, for the duration of the experiment shown in shaded region. Solid linesrepresent observed rip current events. Also shown is the time of the data presented in Figure 6.

Figure 6. Turbulent dissipation rate from a 2 MHz Dopbeam sonar mounted parallel to the beach 0.4 mabove the seabed. Superimposed on these data is the water depth at location of instrumented frame(smooth black and white line). Also indicated are two rip current events, one of which is expanded inFigure 11.


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reaches several hundred dB m�1, blocking all incoming100 kHz sound.

4.1. Stationary Bubble Wall

[26] On the basis of the assumption of a linear bottomslope of 1:33 and using the tidal information from the end ofthe pier the range-dependent bubble wall data presented inFigure 5 were transformed into local water depth-dependentdata. The seaward edge of the bubble wall is typicallylocated in water depths between 2 and 3 m during stationarywall conditions, increasing to 4–5 m during periods withsignificant rip current activity during conditions with amobile bubble wall.[27] The entrained bubbles that make up the bubble wall

are a result of wave breaking in the surf zone, the dynamicsof wave breaking and the exact location of breaking willdepend on the incident wave field, the bottom bathymetry,and the local current field. Video recordings of the surf zoneduring short sections of the experiment confirm that thelocation of breaking is highly variable as waves of differentheights and periods reach their steepness limit. Using the

Rayleigh distribution as a model for the wave heightprobability distribution the relationship between the signif-icant wave heights from the CDIP data and the RMS waveheights at the end of the pier were expressed as Hrms = 0.7Hs

[Thornton and Guza, 1983]. Shallow water wave theorymakes is possible to explore the relationship between thelocation of the stationary bubble wall and the incomingwave field. The change in RMS wave height between theend of the pier, Hrms and the location of the stationarybubble wall Hrms1, due to shoaling (without refraction anddissipation) obtained from an energy balance is

Hrms1 ¼ffiffiffiffiffiffifficpH

cph

rHrms; ð5Þ

where cpH =ffiffiffiffiffiffiffiffigdH

pand cph =

ffiffiffiffiffiffiffigdb

pare the shallow water

phase speeds at the end of the pier (water depth dH) and atthe location of the bubble wall (water depth db) respectivelyand g is the gravitational acceleration. In Figure 8 theaverage water depth at the location of the bubble wall isplotted against the averaged local RMS wave height. Theaverages are over all periods with stationary bubble wall,varying from about 30 min to more than two hours. Thesolid fitted line has a slope of 0.1 and for comparison therelationship between RMS wave height at time of breakingand local water depth found by Thornton and Guza [1983]for Torrey Pines, California (Hrms1 � 0.42db), has beenincluded as a dashed line. Assuming that the conditions foronset of breaking is similar between these two beaches, onesees that the bubble wall moves seaward with increasingwave heights faster than the location of dominant wavebreaking. This may be due to the relative importance ofindividual larger waves breaking in deeper water andcontaining large numbers of bubbles or due to offshoreflows, such as undertow, moving the bubbles seaward.[28] Stationary bubble walls are generally associated with

lower incident wave energies in general and with lowerenergy at lower frequencies in particular (Figure 3). Theseperiods accounted for about 28% of the conditions duringthe 6 weeks of the experiment. It can be assumed that thispercentage varies seasonally with the wave climate,decreasing as the storm rate increases. These results mayrepresent an upper limit to the extent of stationary bubblewall occurrences at Scripps Pier. When the wave energieswere lowest, situations were observed in which part of theacoustical energy propagated beyond the bubble wall,suggesting that the energy associated with the waves wasnot sufficient to mix the bubbles all the way to the seafloor.

4.2. Mobile Bubble Wall and Rip Currents

[29] Whereas the periods with a stationary bubble walloccur during relatively low sea states and in the absence oflow-frequency waves, the periods where the bubble wallmoves over several tens of meters occur during a broadrange of wave conditions. In general, the mobile bubblewalls were found to be less distinct in the backscatterimages and are associated with increased incident waveenergy. It would appear that excessive turbulence fromwave breaking, or the variation in breaking depth due to amore fully developed sea state, results in a less clearlydefined bubble wall. Alternatively, the characteristics of thebubble wall may only appear to be less distinct because of

Figure 7. (a) Scattering cross section per unit volume, Mv

(m�1), calculated from the in situ resonator bubble sizedistribution measurements at the instrumented frame, and(b) the corresponding values from the 100 kHz backscattersonar at the same distance from the beach as theinstrumented frame. Because the sonar was not calibrated,the Mv values presented have been scaled by the maximumMv values obtained in Figure 7a. The sonar data have beenshifted by 140 s to compensate for difference in location ofmeasurement volumes based on alongshore current speedmeasured with the Dopbeam sonar. Dashed vertical linesindicate large bubble injections observed at the surf frame.(c) Attenuation at 100 kHz in dB m�1 calculated from thesize distributions used in Figure 7a.


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the acoustic shadow generated by the blocking effects ofwave breaking.[30] The rip currents can be observed in the backscatter

data as slanted stripes of enhanced intensity and typicallythere is little or no backscatter from regions beyond theseareas (Figure 4b). The acoustic signature of rip currents inthe backscatter intensity images is present only duringperiods with mobile bubble walls, which represent 50% ofthe complete data set. During the 6-week monitoring period246 clearly defined rips were identified. The presence of ripcurrents was confirmed by visual observations in whichobjects or foam was seen moving steadily seaward. Waveheights are also lower and the waves are clearly choppier inrip currents. The observed rip current events have beensuperimposed on the local bubble wall spread in Figure 5. Amajority of the rip currents were focused around a six hourperiod near high tide with a significant number occurringafter the high tide mark. For comparison Smith and Largier[1995] reported more rips during the midtide periods. Thecombined wave energy and rip current data shown inFigure 3 suggest that the probability of observing rip currentevents is higher during periods with significant energy inlower-frequency (<0.1 Hz) waves.[31] Several important rip current characteristics can be

obtained from the backscatter intensity data. A measure ofthe duration of the current can be inferred from the time anoffshore moving event is observed as a significant break inthe location of the bubble wall until the time the bubble wallis reestablished. The speed of the current can be estimatedfrom the slope of the high-scatter regions in backscatter

versus time and range images, and from the example inFigure 4b it is clear that this speed changes with time andtherefore location. Statistics for the 246 clear rip currentevents have been summarized in Figure 9. The meanoffshore current speed distribution, averaged over theduration of the events is about 8 cm s�1. These results arein agreement with earlier observations on the north side ofthe pier [Vagle et al., 2001] but significantly lower than themean advancement speed of about 20 cm s�1 and maximumspeeds up to 70 cm s�1 reported by Smith and Largier[1995] from the same area. The duration of each of theevents are shown in Figures 9b and 9c. Their lifetimes varybetween 5 and 45 min with the most common durationbeing approximately 10 min. The scatterplot in Figure 9d,showing the current speed as a function of water depth hassignificant scatter but a trend toward higher velocities closerto shore. This is in agreement with the idea that the currentsthat start out as narrow jets diffuse both horizontally andvertically as they move away from the surf zone, resultingin reduced flow speeds. Smith and Largier [1995] suggestthe slowing down and stalling of rip currents as they enterdeeper water is due to the onshore propagation of internalwave surges.

4.3. Bubble Wall Turbulence

[32] The turbulence dissipation levels, e, measured 0.4 moff the seafloor has a strong dependence on the local waterdepth variability associated with passing waves. Figure 10ashows a 60-s record of the water depth at the location of theinstrumented frame as obtained from the closest pressure

Figure 8. Root mean square wave height calculated from equation (5) versus the water depth at thelocation of the bubble wall for periods with stationary bubble wall. The fitted solid line has a slope of 0.1.The dashed line represents the relationship between RMS wave height and water depth at the onset ofbreaking as reported by Thornton and Guza [1983] from Torrey Pines, California.


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sensor in the SIO pressure array (approximately 80 mseaward) shifted by 16.5 s and scaled for shoaling wavesusing (5). The 16.5 s shift correspond to a mean wave speedof 4.8 m s�1, which is in good agreement with a shallowwater phase speed of 4.4 m s�1 using a mean water depth of3 m. The closely correlated e values have been plotted inFigure 10b and over a wave period there is a more than twoorders of magnitude change in the observed turbulencedissipation levels from 2 � 10�6 m2 s�3 to more than2 � 10�4 m2 s�3. When averaged over many wave periods eshows a clear logarithmic local water depth relationship(Figure 10c). Because the measurements were made in thebubble wall, tens of meters offshore of the breaking zone,these turbulence levels cannot be a direct result of thebreaking process. (When the active breaking zone extendedto the location of the instrumented frame signal saturationwas observed at the acoustical resonator (Figure 7)). Anexplanation for these observations might be increased wavebottom boundary turbulence associated with the wavetroughs diffusing up to the location of the sensor at 0.4 mfrom the bottom.[33] The presence of the rip current event shown in

Figure 11 was confirmed by the backscatter intensity datashown in Figure 11e in which the rip can be observedaround minute 42 when the offshore velocity is approxi-mately 0.02 m s�1. It takes another 8 min before the ripcurrent reaches the instrumented frame sensors, 17 mfurther north. At minute 44 the current speed increases toa steady 0.11 m s�1 for the next 10 min. Analysis of

independent video recordings also confirm the presence ofthis rip current where it shows up as a steady flow of debrisand foam moving offshore at about 0.1 m s�1. During thisrip event the measurable alongshore current observed atthe instrumented frame increased to nearly 0.6 m s�1 ina northerly direction and persisted for nearly 10 min(Figure 11c).[34] During the initial period of this rip event e, (0.4 m

above the seabed) increased and the time averaged variabil-ity in e decreased dramatically (Figure 11a). Also, thestandard deviation of the horizontal velocity along eachindividual Dopbeam profile su, which will be used laterto model the evolution of the bubble field in the presence ofa rip current, increased rapidly from about 0.005 to0.02 m s�1 and then decreased slowly over the next10 min (Figure 11b). The corresponding air fraction asobtained from the acoustical resonator on the frame hasbeen plotted in Figure 11d.[35] Horizontal diffusion of the turbulence may play an

important role in the inner region of the surf zone [Battjes,1983]. However, Svendsen [1987] argues that the horizontalgradients of the turbulent kinetic energy are so small that thehorizontal transport of turbulence is dominated by convec-tion due to the relatively strong undertow current. Obser-vations show that this current could be as much as 10% ofthe wave celerity approximately one third of the depthabove the bottom [Svendsen, 1984; Hansen and Svendsen,1984]. However, even with this high value it would take avortex five wave periods to move half a wavelength.

Figure 9. Rip current statistics for the 246 events observed during the 6-week period. (a) Probabilitydistribution of the mean current speed over the lifetime of (b and c) the events and (d) the current speeddistribution as a function of water depth for the same events and time spans.


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Therefore the dissipation of the kinetic energy will occur atthe place where the turbulence is generated [Svendsen,1987], and it is therefore unlikely that the observed turbu-lence is a direct result of the wave breaking.

4.4. Bubble Field Evolution During a Rip CurrentEvent

[36] The 100 kHz sounder system gives informationabout the scattering characteristics of the surf zone bubblefield and indicates the presence of rip events but gives noinformation about the size distribution of bubbles in thisfield. However, Dahl and Jessup [1995] and Vagle andFarmer [1998] related Mv and the total air fraction in bubbleclouds using observed bubble size distributions. The acous-tical resonator on the surf frame collected information aboutthe bubble size distribution during three 5-hour periodsstraddling high tide. The results show a significant differ-ence in the size distribution between the bubble fields in the

presence of rip currents and breaking waves as compared tothe field within the bubble wall not associated with a ripcurrent. Figure 12 shows a volume scaled size distributionwith maximum air fraction of 3.5 � 10�5 obtained duringthe rip current event shown in Figure 11, corresponding toMv = 2.5 m�1. The dominant bubble radius in the rip currentis between 80 and 100 mm and there are many bubbles withradii greater than 200 mm. In contrast, within the mainbubble wall the dominant bubble radius is closer to 40 mmair and very few bubbles with radii greater than 100 mm arepresent (Figure 12a). Also, the total air fraction is 10�7,corresponding to Mv � 0.1 m�1. Both bubble size distribu-tions shown in Figure 12 were averaged over 10 s.[37] The evolution of the bubble field in the bubble wall

with and without rip currents can be studied using a modelthat combines bubble buoyancy and dissolution with themeasured turbulence levels. The bubbles were considered ashaving a surfactant coating at all times [Thorpe, 1982].

Figure 10. (a) Sixty-second record of water depth at the site of the instrumented frame obtained fromthe closest pressure sensor in the pressure array shifted by 16.5 s and scaled for shoaling waves using (5).(b) Corresponding turbulence dissipation, e, from the 2 MHz Dopbeam sonar at a distance of 0.4 m abovethe seafloor. (c) Turbulence dissipation rates, e, as function of water depth averaged over 60 min.


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Thorpe [1982] developed an approach, which includes boththe bubble dynamics and the gas flux across the surface ofindividual bubbles made up of oxygen and nitrogen. De-tailed information about the model are given by Thorpe[1982] and by Vagle et al. [2001].[38] In this model the time rate of change of bubble

radius, a, can be expressed as a result of gas diffusionand changing hydrostatic pressure,

da

dt¼ �1

3pþ 4g=að Þ3RT

aD1f1N1 x pþ 2g

a

� �� p10

� ��

þ D2f2N2 1� xð Þ pþ 2g

a

� �� p20

� ��þ a

dp

dt

ð6Þ

and

dxdt

¼ 3RT

a2 pþ 2g=að Þ D2f2N2x 1� xð Þ pþ 2g

a

� �� p20

� ��

� D1f1N1 1� xð Þ x pþ 2g

a

� �� p10

� �ð7Þ

where p + 2g/a is the pressure of the gas inside the bubblewith surface tension g, p10 = xp0(1 + 100s1) with s1 beingthe saturation level of oxygen, p20 = (1 � x)p0(1 + 100s2)with s2 being the saturation level of nitrogen, p = p0 + rgz,p0 is the ocean surface pressure, g is the gravitational

Figure 11. (a) Turbulent dissipation rate e from the Dopbeam 0.4 m above the seabed. (b) Standarddeviation su of the horizontal velocity profile over a 0.8 m path length from the Dopbeam. (c)Corresponding alongshore current speed (southerly current positive). (d) Air fraction as calculatedfrom bubble size distributions obtained 1.5 m from the seafloor. The open squares indicate modeledair fraction data due to buoyancy, dissolution, and turbulence. (e) Backscatter intensity data from the100 kHz sonar. The dotted black line at 160 m indicates location of in situ sensors and data inFigures 11a–11d.


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acceleration, r is the water density and rgz is the addedhydrostatic pressure for a bubble at depth z, N is the Nusseltnumber, fi is the coefficient of gas absorption, x = 0.215 isthe mole fraction of oxygen, R is the gas constant, and T isthe temperature.[39] For a bubble rise speed wb, and instantaneous verti-

cal component of random turbulent velocity w0, the actualascent rate will be

dz

dt¼ w0 � wb ð8Þ

or

dp

dt¼ gr w0 � wbð Þ: ð9Þ

The terminal velocity of a bubble, wb, can be obtained fromthe balance between drag and buoyancy forces

CD

pa2

2rw2

b ¼ rg4p3a3 ð10Þ

where CD is a drag coefficient [Keeling, 1993]. For bubbleswith radii greater than 560 mm the rise speed is assumed tobe constant (0.3 m s�1) [Levich, 1962]. For the turbulentvertical flow velocity w0 the range averaged standarddeviation su from the Dopbeam sonar at 0.4 m was used(Figure 11b) with the assumption of isotropic turbulence.Equations (6)–(10) were solved numerically using a fourth-order Runga Kutta method from t = 0 to t = tt with an initialbubble size distribution as a function of depth. Theequations were solved for each depth and each bubble sizeincrement individually and added to the individual bubbleradius and depth bins at t = t1.[40] The bubble wall size distribution is in good agree-

ment with model results in which buoyancy, dissolution,and turbulence effects are considered following an initialinjection of bubbles with size distribution proportional tobubble radius to the power �3 as indicated in Figure 12a[Vagle et al., 2001]. Buoyancy sorting of recently formedbubble plumes reduces the number of larger bubbles, andthe bubble density rapidly decreases with time and distancein an offshore or alongshore current. It is interesting to notethat the observed and modeled dominant bubble radius inthe bubble wall has a resonant frequency close to 100 kHz,resulting in maximum blocking of acoustical propagation atthis frequency. The modeled time evolution of the bubblefield throughout this rip current event also agrees well withthe observations as can be seen in Figure 11d. In Figure 11dthe open squares indicate the modeled air fraction as afunction of time using the model and input parametersdiscussed above.[41] Figure 12b shows the corresponding frequency-

dependent attenuation, ab for the two observed bubble sizedistributions from Figure 12a. In the bubble wall themaximum attenuation will occur at frequencies between70 and 80 kHz with attenuation levels close to 4 dB m�1,while in the wave breaking dominated rip current themaximum attenuation takes place at frequencies between20 and 50 kHz with levels as high as 450 dB m�1. It isworth noting that at 12 kHz the attenuation was estimated atclose to 26 dB m�1, which agrees favorably with the valuesreported by Deane [2000] from measurements in the surfzone.[42] From the sonar records it is unclear whether a

nearshore bubble wall was present during this time sincethe high concentration of bubbles in the rip current effec-tively blocks any sonar signal from inshore of the bubblesadvected by the rip current. However, measurements fromthe surf frame located at a range of 160 m clearly indicatethe presence of bubbles in the waters further onshore(Figure 11d) suggesting total blockage of the acousticalsignal.[43] Advected bubble clouds in rip currents have previ-

ously been shown to produce noticeable attenuation of high-frequency propagation paths [Caruthers et al., 1999] and acomprehensive discussion of bubble cloud evolution withinrip currents is treated elsewhere [Terrill, 1998; Terrill and

Figure 12. (a) Ten-second averaged volume scaled bubblesize distributions from within the rip current event shown inFigure 11 and a typical example of the measureddistribution in the bubble wall as measured with theresonator on the surf frame. The vertical arrow representsthe resonant bubble radius at 100 kHz, and the dashed lineshows the expected slope of the bubble size distribution atinjection. (b) Corresponding attenuations as functions ofacoustic frequency calculated from the size distributions inFigure 12a using (6).


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Melville, 2000; Vagle et al., 2001]. Buoyancy sorting of thebubbles caught in rip currents tends to reduce the number oflarger bubbles and the bubble density rapidly decreases withdistance offshore.

5. Conclusions

[44] Six weeks of backscatter intensity measurements ofthe bubble field in the surf zone at Scripps Pier and short-term in situ measurements of the quiescent bubble sizedistributions and turbulence energy dissipation have beenused to examine the dynamics of the surf zone. The datashow that the consistent bubble field, or bubble wall,behaves differently depending on the presence or absenceof rip current activity. Clear bubble wall was observed in68% of the data. A stationary bubble wall (18% of the data)varies slowly with location following a water depth contourwhich is a function of the height of the incoming waves, butnot necessarily coincidental with the expected location ofwave breaking. During the experiment no significant stormsimpacted the area, and the data suggest that the transitionfrom a stationary to a mobile bubble wall might to beassociated with the presence or absence of low-frequency(<0.1 Hz) waves.[45] Measurements of the near bottom turbulence in the

bubble wall (0.4 m above the seabed) show significantvariability and strong dependence on local water depth.Also, the presence of rip current events increases the overallturbulence dissipation levels and decreases the variability.[46] The bubble size distribution differs significantly

between the bubble walls seen in rip currents and thoseseen in the absence of recent breaking events. Because ofthe enhanced turbulence levels in the rip currents a signif-icant proportion of larger bubbles are suspended longer inthe water column, and show a bubble radius of maximumvolume scaled size density being close to 100 mm. In theabsence of this intense turbulence the bubble size distribu-tion rapidly diminishes because of buoyancy and dissolu-tion and the radius of maximum air fraction reduces to40 mm with fewer larger bubbles present. The evolution ofthe bubble field agrees closely with model calculations inwhich buoyancy, dissolution and turbulence effects havebeen included. The scattering cross section per unit volumeand the overall attenuation of these bubble clouds are high,resulting in frequent blocking of the sonar signal. Enhancedturbulence mixes the bubbles throughout the water columnadding to the effectiveness with which the bubbles blockacoustical signals.

[47] Acknowledgments. The Office of Naval Research High Fre-quency Acoustics Program supported this work. We gratefully acknowledgethe support of the many individuals who contributed to the research,especially Grant Deane, Dale Stokes, and James Uyloan from SIO andJim Preisig from WHOI. The invaluable help from Nick Hall-Patch andRon Teichrob from the Ocean Sciences Division at IOS is also greatlyappreciated. We also appreciate the useful comments from the reviewers.

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��P. Chandler and S. Vagle, Institute of Ocean Sciences, 9860 West Saanich

Road, Sidney, BC, Canada, V8L 4B2. ([email protected])D. M. Farmer, Graduate School of Oceanography, University of Rhode

Island, Kingston, RI 02881, USA.


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On the dense bubble clouds and near bottom turbulence in the surf zone

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