Observations of underwater sound from laboratory breaking waves and the implications concerning ambient noise in the ocean

Observations of underwater sound from laboratory breaking waves and the implications concerning ambient noise in the ocean

Ali R. Kolaini

National Center for Physical Acoustics, University of Mississippi, University, Mississippi 38677

Lawrence A. Crum

Applied Physics Laboratory, University of Washington, Seattle, Washington 98105

(Received 11 January 1994; accepted for publication 22 March 1994)

The results of an experiment to characterize the underwater sound field radiated by various breaking waves intensities in fresh water in the range from 0.1 to 20 kHz are described. Waves are generated by a computer-controlled plunging-type wave maker and propagate along a 12.7-m-long channel where they are made to break at the mid-surface of a 3-x3-x2.5-m anechoic water tank. The individual bubbles and bubble clouds entrained by the breaking wave provide a mechanism for sound production. Using high-speed cinephotography, correlations were established between the hydrodynamic evolution of the cloud and the radiated acoustic emissions. The bubble size distributions inside the cloud were measured with the aid of a high-speed video camera and a fiber optic cable. These measurements indicate that single bubbles with radii as large as 7-8 mm may be entrained in this fresh-water system by moderate spilling breakers. Detailed measurements of the bubble size distribution of the bubble cloud enabled us also to obtain a measurement of the average void fraction in the cloud. These observations reveal that the sources of sound in laboratory spilling breakers is due mostly to single bubble oscillations that can have frequencies as low as 400 Hz; in the case of plunging breakers, it appears that both individual bubbles and bubble clouds can contribute to the acoustic emissions. The acoustic radiation from bubble clouds is the result of

collective oscillations of the bubbles, stimulated by large scale vortices created by the plunging breaker. The sound spectra, averaged over 100 breakers, reveal the following observations. First, the peak frequencies of the average sound spectra shifts from few kHz (weak, spilling breaker) to few hundred Hz (plunging breaker). Second, the sound pressure levels increase in all frequency bands with increasing breaker severity. Lastly, the high-frequency portions of the sound spectra have slopes of about 5-6 dB/oct, which are the slopes observed for the noise spectra of the ocean. These results provide considerable insight into the likely source mechanisms for ocean ambient noise.

PACS numbers: 43.30.Nb, 43.30.Lz

INTRODUCTION

Over the years, considerable attention has been devoted to the understanding of ambient sound in the ocean. The earliest measurements of ambient-sound spectra levels in the ocean were reported by Knudsen et al. (1948). They demonstrated that the sound spectral level depends strongly upon wind speed and decreases with increasing frequency at the rate of approximately 5 dB/oct. Later, Wenz (1962) reviewed the data from Knudsen et al. and suggested that gas bubbles generated by breaking waves are a major contributor to underwater noise. Recently, several international conferences have been devoted to the understanding of the source mechanisms for ambient noise production at the sea surface (Ker- man, 1988, 1993) and have lent further support to the contributions of gas bubbles as the principal source of this noise. However, a detailed description of the specific roles of these bubbles has not yet been given.

Recently laboratory studies of breaking waves were reported by Medwin and Beaky (1989), and by Medwin and Daniel (1990); in these studies, the sound generated by gently spilling breakers was measured. This sound consisted of a

superposition of damped sinusoidal pressure waves. They concluded that the noise radiated by these breakers resulted from newly created bubbles oscillating at their natural resonance frequencies. The same conclusion was arrived at by Banner and Cato (1988), in which they produced laboratory breaking waves by towing a hydrofoil in a channel. Upde- graff (1989) has studied the sound radiated by gently spilling breaking waves in the ocean and concluded that the radiated sound was also composed of damped bubble oscillations. Laboratory measurements of noise generated by stronger breaking waves have been made by Kerman (1988), Papani- colaou and Raichlen (1988), Melville et al. (1988), and Loe- wen and Melville (1991). In all these cases, absolute sound pressure measurements were not obtained because of tank reverberation. For waves of moderate slopes, Loewen and Melville (1991) showed that the acoustic energy radiated by breaking waves was correlated with the mechanical wave energy dissipated during the breaking process.

Measurements of noise generation by breaking waves at sea were recently reported for which the contributions from distance sources were eliminated by using a vertical array of hydrophones instead of omnidirectional ones (Shonting and

1755 J. Acoust. Soc. Am. 96 (3), September 1994 0001-4966/94/96(3)/1755/11/$6.00 ¸ 1994 Acoustical Society of America 1755

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Taylor, 1988; Carey et al., 1990; Kennedy, 1992; Chapman and Cornish, 1993; Hollett, 1994). Farmer and Ding (1992) used a horizontal array deployed near the surface to track individual breaking waves. In these reports the source levels measured directly above the array show a correlation between wind speed and noise intensity. At frequencies below a few hundred Hz, their ambient noise measurements show the presence of locally wind-generated noise without contamina- tion from shipping (Carey et el., 1990). These results suggest that at the lower frequencies there exist two wind-speed- dependent regimes: One prior to onset of wave breaking, and another after wave breaking has commenced. The existence of the two wind-speed regimes was also confirmed by Chap- man and Cornish (1993). Recent open-ocean measurements of the noise generated by breaking waves (McConnel et el., 1992; Chapman, 1991; Kennedy, 1992), the laboratory measurements of noise generated by transient water jets (Kolaini e! el., 1991, 1993), and the tipping-trough experiments by Carey e! el. (1993) suggest that the frequency of the noise could range as low as several tens of Hertz. Indeed, measurements by McCreery et el. (1993) near Wake Island have demonstrated wind-dependent noise at frequencies as low as 4 Hz! Since breaking waves produce sound at low frequencies, the collective oscillations of bubbles within bubble clouds were proposed as the source of low-frequency ambient noise (Prosperetti, 1988a; Carey and Browning, 1988). It is generally assumed that large bubbles are not present in breaking waves, especially in salt water, and thus the source of the noise generation below 1 kHz was thought to be due to collective oscillations. Laboratory and analytical studies of noise from cylindrical bubble columns by Yoon et el. (1991), Lu et el. (1990), and Nicholas et el. (1994) have lent further credibility to this hypothesis.

In addition to the numerous experimental studies, there have been several recent theoretical analyses of noise generation by breaking waves. These theoretical calculations given by Prosperetti (1988b), Carey and Browning, (1988), Longuet-Higgins (1990), and Crowther (1988) have suffered from a lack of knowledge of the characteristics (size, number, distribution) of bubbles created by the breaker. Thus these models typically predict only the general behavior of the noise levels in terms of slopes and order of magnitude estimates. Recently, O•guz (1994) has proposed a model based on collective oscillations of bubbles to predict the absolute noise levels; in this case, detailed knowledge of the individual characteristics of the entrained bubbles is not criti-

cal.

In the following sections of this article, we report measurements of the absolute sound pressure levels obtained for various breaker intensities. In these measurements, we were

able to reproduce carefully the conditions for each breaking wave event and also average 100 separate events. The radiated spectral densities for various breaker intensities demonstrate a falloff of about 5 dB/oct from a few hundred Hz to

25 kHz. This behavior parallels that displayed in the Knudsen-Wenz spectra for ambient noise in the ocean. Fur- thermore, the more intense breakers produced in our laboratory demonstrate the existence of low frequency acoustic emissions indicative of the collective oscillations of bubble

Hydraulic

2' x 2' x 32' Flume Section

4'x4'x8'

Flume Section

8'x 12' x 12' Main Tank

FIG. 1. Schematic drawing of the research wave maker/anechoic tank facility (not drawn to scale).

clouds. Thus the data that are presented here should provide us with some insight into the complex acoustic behavior of ocean breaking waves.

I. EXPERIMENTAL PROCEDURES

The experiment was conducted in an unique combina- tion anechoic tank and wave making facility. A plunging- type, wedge-shaped wave maker was mounted at one end of the 0.7 m x0.7 m X 12.7 m flume which was ultimately connected to a 2.5 m X 3 m X 3 m anechoic tank (see Fig. 1). This wave maker was operated by a hydraulic piston actuator which was guided by a state-of-the-art Parker D31F proportional valve. The proportional valve was operated via a Parker EZ00595 electronic controller which is connected to a

personal computer. This system enabled us to produce gravity waves that would break at any user-specified location near the end of the flume or at any location within the tank. The hydraulic cylinder employed an electrohydraulic actuator with a linear displacement transducer to provide feedback for controlling the motion of the cylinder. Breaking was caused by the local concentration of wave energy, created by generating longer waves (with lower frequencies and higher velocities) overtaking shorter waves (with higher frequencies and lower velocities), a technique originally suggested by Longuet-Higgins (1974). The bottom and walls of the tank were lined with 82-cm high redwood wedges with 30 cmX30 cm bases; these wedges have a large acoustic ab- sorption. For the detail acoustical characteristics of the anechoic tank refer to Kolaini and Ahmadian (1994). The facility contained tap water to a depth of 46 cm in the flume section, and to a depth of about 2.3 rn in the anechoic tank section. The motion of the wave maker was computer- controlled and was immediately terminated after generation of the wave group. This technique eliminated all noise generated by the hydraulic pump, and structural vibrations generated by the motion of the wave maker.

The sound emission from bubble clouds generated by breaking waves was measured using a B&K 8105 broadband hydrophone with a plane wave sensitivity of -208.5 dB re: 1 V/ttPa, which was connected to a MIO A/D board via a B&K 2635 charge amplifier, and was high-passed filtered above 100 Hz using an analog filter. The A/D board was triggered by the hydrophone output. The digitization speed and conversion gain were (100 000 samples/s) and 12 bits, respectively. The recorded data were transferred to a Macin-

1756 J. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 A.R. Kolaini and L. A. Crum: Observations of underwater sound 1756


tosh II computer via LabView soft/hardware for further analysis. The evolution of the bubble cloud in the tank was recorded with a Photec IV rotating-prism motion picture camera with two lenses operating with a speed of 1000 frames per second. These cinephotographic studies enabled us to correlate events in the evolution of the breaking wave with the associated acoustic emission. The bubble size dis-

tribution within the clouds was measured using an 1FllD4- A20S Olympus fiberscope lens with a depth of field of 1 cm connected to a high-speed Kodak Eckta-Pro video camera, typically used at a framing rate of 500 frames/s. The high- speed video camera was triggered at the instant when the cloud cross-sectional area has reached its maximum growth. A small thin plate was placed in front of the lens 2 cm from it to capture bubbles in a volume of 2x2x 1 cm at a time. By moving the fiberscope to new locations we were able to map the bubble population and void fraction of the entire cloud.

The wave surface elevations were measured with capaci- tance type wave gauges made of 36 a.w.g. polythermalized insulated wire and placed in the middle of the flume. The surface displacement data was sampled at 2500 samples per second and was low-passed filtered at 50 Hz. These gauges were calibrated prior to each experimental run by sampling the quiescent water level and then displaying them at 1-cm increments to new water levels. A polynomial curve was fit- ted to these data, thus giving us a calibrated equation relating gauge voltage to wave amplitude.

The acoustic reverberation characteristics of the

anechoic tank were determined using the peak response method with an underwater source and broadband excitation.

The underwater source was kept in a fixed location in the tank and a B&K 8105 hydrophone positioned very close to the source where it received only the source response. The tank was divided into a three-dimensional grid with an incre- mental cube of 15x15x15 cm. Another B&K 8105 hydrophone was placed in the grid locations, where the response of the tank and the source could be measured. The transfer

function between the two hydrophones was used to identify the tank reverberation. A model analysis STAR software package was used to calculate the modal shapes within the tank. The inputs for the modal analysis package were the sharp peaks in the transfer function that were measured in various locations within the tank. Figure 2(a) and (b) show examples of the modal shapes computed using this program. These modal shapes were measured at the water depth of about 45 cm and have shape frequencies of about 540 and 950 Hz, respectively. These were the only modal shapes below 1 kHz that we were able to identify in the tank.

A series of wave groups was produced that would break with various intensities in the middle section of the anechoic

tank. The time series of the surface displacement prior to breaking was then correlated with the acoustic emissions from the subsequent bubble clouds. The relationships between the breaking-wave intensity (obtained from the surface displacement gauge) and acoustic emissions (obtained from the hydrophone) provide the basis for our analysis.

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FIG. 2. Modal shapes of the anechoic tank reverberations at the depth of 45 cm from still water surface below 1 kHz: (a) 540 Hz, and (b) 950 Hz; these appear to be the only forms that can be excited in our frequency range of interest.

II. RESULTS

The wave-breaking process and the subsequent mechanical radiation is a coupled hydrodynamic and acoustic problem. It is well known that significant turbulence is generated within and under the breaking wave. The production of turbulence begins with the steepening of the wave crest. The particle velocity of the crest increases as the wave steep- ens, causing the wave to pitch forward once it exceeds the wave phase velocity. Depending on the initial conditions of the jet created at the crest, a spilling or a plunging breaking wave may result. We have determined that the underwater ambient noise generated by the breaking wave depends on the nature of the air entrainment. There are two separate mechanisms that lead to acoustic emissions. First, sound may be generated by the entrainment of individual bubbles, which subsequently radiate at their natural resonance. Second, the individual bubbles within the cloud may oscillate coherently in a collective mode. Typically, the frequency radiated by individual bubbles is much higher than that radiated by the cloud [see, Yoon et al. (1991) or Nicholas et al. (1994)]. Of course, these mechanisms are not mutually exclusive and may coexist.

Figure 3 shows a time series of the surface displacement in a wave packet leading to a moderate spilling breaker at different locations down the flume. Time series similar to

these can be used to estimate the momentum and energy flux of the wave group (Melville and Rapp, 1985). The conver- gence of wave energy in the neighborhood of a single point and the build up of wave amplitude in which breaking waves may occur is evident from this figure. The last wave form, at about 13.41 m from the wave maker, was recorded just be-



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FIG. 3. Time series of the surface displacement at various locations down the channel for a moderate spilling breaker. Note the movement of low frequency wave toward the high frequency one. At the 13.41-m position, the wave has become steep enough to break. Via this process, breaking waves could repeatedly be produced at predetermined locations within the anechoic portion of the tank.

fore the onset of the moderate spilling breaker. The most sensitive parameter for controlling the occurrence of a breaker is the dimensionless parameter, aiki, where a i is the amplitude of the ith wave component and ki=(2rrfi)2/g, where fi is the frequency of the ith wave component. The onset of the breaker depends on a threshold value of a iki . By increasing a ik i beyond the threshold value, single spilling breakers of various intensities were produced in the vicinity of a fixed point. A subsequent increase in aiki led to a single plunging event. In some of the plunging-type breaker events, weak multiple breakers would occur prior to a single prominent breaker.

A series of high-speed photographs of a strong spilling breaker giving rise to the entrainment of gas bubbles is shown in Fig. 4. The frames are sequential, but not consecu- tive; the frame number, with "0" as the first frame, is given as a label on the left of each frame. Since the framing rate was 1000 frames/s, these labels represent the elapsed time in milliseconds. The vertical line on the left side of each image is a simultaneous picture of "sound," obtained by photo- graphing the oscilloscope trace generated by a hydrophone located beneath the breaker. The water surface was marked

in the first image to clearly indicate its location. On the top right corner of the first few images, it is clear that the waves have already spilled over the front face of the wave crest (see the indicator). The plunging water jet, which entrains gas bubbles, is evident from the first few frames. The gas bubble entrainment process of a spilling breaker is accompanied by

a deceleration of the particle motion by the upward slope of the orbital velocity in the wave and acceleration by entrained water in the whitecap. The whitecap region has turbulent velocity fluctuations and there exists vorticity to support the entrainment of both air and water in the field but is most

probably concentrated at the leading edge of the spilling breaker.

The first detectable sound, which is above background noise, was received 93 ms from the onset of the breaker, where, it appears, the vorticity at the leading edge has trans- ported air into the water. It appears that these initial acoustic emissions are the result of newly created bubbles that have been stimulated into volume pulsations. This process contin- ued as air was continuously entrained and acoustically active bubbles of various sizes were created. The generation of acoustically active bubbles are evident from frames #223- 251, where frequencies of about 0.5-1.5 kHz were emitted at the early stages of the air entrainment process. The existence of a larger bubble is shown in frames 376-482 ms (see the indicator in frames #416-428). The noise generation by this bubble is not the corresponding acoustical signal shown in frames #426-431. Nevertheless, a bubble of approximately 6 mm in radius was generated by breaking waves. Since we are only imaging the plane view, the one to one correspon- dences between the bubble generation and acoustic emissions may not be possible. However, the correlation between the acoustic radiation and air entrainment process of spilling breaker shown in Fig. 4 serves to identify some of the fea- tures of the sources of ambient noise. Because of the com-

plexity of the breaking process, it is difficult to visually identify each individual acoustic source, but Fig. 4 gives some insight into the mechanisms for gas bubble entrainment that lead to sound radiation. It is important to note that the large bubbles observed here are characteristic of fresh water; typically, in salt water, much smaller bubbles are produced and, it is generally believed, bubbles on the order of 1 cm in diameter are not produced.

In the case of a plunging breaker, the visual observations reveal different hydrodynamics and bubble acoustics. In this case, once the particle velocity at the wave crest exceeds the phase velocity of the wave, the jet plunges onto the front face of the crest with a relatively large kinetic energy. The jet falling onto the wave surface, moving from right to left, develops a hydrodynamic condition which is composed of two large vortices, one revolving clockwise, the other coun- terclockwise. The clockwise vortex containing bubbles can cause the liquid surface to rise to a level higher than the unbroken wave crest elevation. Frame-by-frame analysis of the high-speed motion picture shows that the counterclock- wise (CCW) vortex may form a cylindrical bubble cloud which, due to the dynamics of eddy, may detach from the rest of the breaking structure. It appears that this detachment may give rise to low-frequency acoustic emissions through collective oscillations of the bubble cloud. It will be seen

later that acoustic emissions with frequencies as low as 100 Hz are seen even in laboratory breaking waves. Since individual bubbles resonating at this frequency are unlikely, we seek a hydrodynamic mechanism for cloud excitation.

In a separate study of mechanism of low-frequency

1758 J. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 A.R. Kolaini and L. A. Crum' Observations of underwater sound 1758


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FIG. 4. Photographs of a sequence of frames from a high-speed movie of a laboratory-generated spilling breaking wave. The original film was made at a speed of 1000 frames/s. The numbers on the left of the frame show frame number and also represent time in milliseconds since frame 0. A strong spilling breaker was designed to break at 12.7 m from the wave maker. The gravity waves are propagating from right to left and photographs show only 60 cmX 100 cm of the breaking wave region. The left-hand portion of each frame shows an oscilloscope trace of the acoustic pressure radiated by breaking wave. By the first frame, the wave has already spilled over the front of the crest. The first detectable sound was received 93 ms from the onset of the breaker, as the leading edge of the wave entrained air into the water. This air entrainment and subsequent bubble formation gives rise to acoustic emissions (93-702 ms). It appears that most of the sound radiated in this breaker is associated with individual bubbles.

acoustic emissions, it was shown that the physical mechanism that drives a bubble plume into oscillation is the existence of a strong axial jet directed downward into the bubble plume and an opposite jet directed upward into the crator formed by the impact of a transient water jet entering the host fluid (Kolaini et al., 1993). The same mechanism (i.e., cloud detachment by the CCW eddy) is the best candidate for bubble excitation created by plunging breaker. The large CCW eddy motion, after bubble cloud detachment, can trans- port the entrained bubbles to a depth on the order of the wave height and, for strong breakers, to even greater depths.

The dynamic processes of spilling breakers are not as dramatic as the plunging case. Based on our cinephotographic studies, spilling breakers do not appear to possess the eddies that are characteristic of the plunging breakers (see Fig. 4). Our acoustic measurements, together with measurements of the size distribution of individual bubbles en-

trained by spilling events, tend to suggest that the principal noise source for these events in fresh water are newly created

bubbles. The transition from individual bubbles to resonating bubble clouds---collective oscillations--is not distinct, but gradual, and is principally related to the intensity of the breaking event. We shall return to this discussion later.

The pressure-time traces of three distinctive breaker intensities are shown in Figs. 5(a), 6(a), and 7(a) for weak spilling, moderate spilling, and weak plunging breakers, respectively. The duration and magnitude of the noise generated by these breakers increases with breaker intensity. The acoustic sampling interval of the breakers was measured to be as low as 0.23 T and as high as 1.20 T, depending upon the severity of breakers. Here T is the period of the center frequency of the gravity waves of typically around 1.1 s. The expanded time sequence of Fig. 5(a) is shown in Fig. 5(b)- (d). The distinctive acoustic events appear to be associated with individual bubbles of various sizes. Figure 6(b)-(d) are the expanded time sequences of Fig. 6(a) for a moderate spilling breaker. Similar to the weak spilling breaker, the individual acoustic events appear to be generated by single



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FIG. 5. Pressure-time traces of a weak spilling breaker, (a) is the entire waveform and (b)-(d) are expanded versions of the waveform (a). Note that the acoustic emissions appear to be associated with individual gas bubbles that are radiating at their natural frequencies and separated in time.

bubbles; in particular: the relatively low-frequency noise generated at the end of the pressure trace is most likely due to a single bubble with a frequency of roughly 600 Hz [Fig. 6(d)]. This is the classical form for the volume pulsation of a bubble with size approximately 1.1 cm in diameter. As will be discussed later, moderate spilling breakers indeed generate bubbles that are as large as 6-7 mm in fresh water. We were able to observe bubbles of this size in our cinephotographic studies and, occasionally, there appeared to be a correlation between their production and the associated acoustic emissions. Finally, the expanded pressure signals of the Fig. 7(a) are shown in Fig. 7(c)-(d) for a plunging breaker. In this case, the observations showed that single bubbles were responsible for acoustic emissions of frequencies above about 500 Hz; below this frequency, collective oscillations of bubble clouds created by large eddies is probably respon-

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FIG. 6. Pressure-time traces of a moderate spilling breaker, (a) is the entire waveform and (b)-(d) are expanded versions of the waveform (a). In this case, many bubbles are produced and the individual bubble events are hard to distinguish. The distinguishable event near the end of the trace is most probably produced by a large single bubble.

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FIG. 7. Pressure-time traces of a weak plunging breaker, (a) is the entire waveform and (b)-(d) are expanded versions of the waveform (a). Again, many bubbles are produced, making individual events difficult to distinguish. An FFT of the later portion of the trace shows components frequencies as low as 200 Hz, implying the existence of collective oscillations.

sible. For example, the 200-Hz signal shown at the end of the pressure-time trace of Fig. 7(d) corresponds to a bubble size of roughly 3.3 cm in diameter. With our cinephotographic system, we were not able to observe bubbles as large as 3.3 cm in the cloud generated by a plunging breaker; therefore, we conclude that frequencies on this order must be emitted by collective oscillations of a bubble cloud generated by the counter-clockwise eddies.

Three-dimensional representations of the power spectra in linear scale versus time and frequency for the pressure traces of Figs. 5-7 are shown in Figs. 8(a)-(c), respectively. These figures demonstrate a shift of the dominant acoustic emission maxima from a few kHz down to a few hundred Hz

as the breaker intensity is increased. Another feature of the time evolution of the linear spectra is their spiky, intermittent nature. Figure 8(a), which corresponds to a "weak" spilling breaker, demonstrates that the dominant acoustic energy is in the 1.5 to 3 kHz region. These frequencies correspond to a bubble radii range from about 1.1 to 2.2 mm, using the fa- miliar Minnaert formulae (Minnaert, 1933). Figure 8(b), which corresponds to a "moderate" spilling breaker, demonstrates intermittent acoustic energies covering a broad frequency range with a dominant spike at around 600 Hz. This frequency corresponds to a bubble size of about 5.5 mm. Our cinephotographic observations demonstrate that it is possible to entrain bubbles as large as 5.5 mm in fresh water. Finally Fig. 8(c), which corresponds to a plunging breaker, demonstrates pronounced peaks at less than 1 kHz as well as sec- ondary maximum above 1 kHz. Note the marked increase in energy below 500 Hz at about 0.5 s after the breaker noise initiation. The intermittent spiky nature of the spectrum below 500 Hz that is generated at later stages of the breaker dynamics, appears to result from both single bubble oscillation, created as bubbles are entrained by the flow, as well as the collective oscillation of a cloud of bubbles that first must

be formed, and then is stimulated into oscillation by the associated hydrodynamics. The rise in sound levels at the



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FIG. 8. Three-dimensional representation of the power spectra in linear scale, (a) weak spilling breaker, (b) moderate spilling breaker, and (c) weak plunging breaker. For the later two breakers, note the evolution in time from high frequencies and low intensities to low frequencies and high intensities.

lower frequencies occurs in the more developed breaker as the cloud runs down the forward face of the wave.

The size distribution of bubbles generated by breaking waves was measured by utilizing a high-speed video camera with a fiber optic cable, enabling views to be obtained of the individual bubbles entrained by the breaker. Figure 9(a) shows the histogram of the bubble size distributions of the weak spilling breaker. Note that a few individual bubbles with radii in the range from 1.1 to 2.2 mm are created, thus producing sizes capable of generating the observed spectra in the 1.5-3.0 kHz range, as shown in Figs. 5 and 8(a). The generation of larger bubbles by moderate spilling breakers is evident from the bubble size histogram shown in Fig. 9(b), which demonstrates the existence of bubbles in the 5.5 mm

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range, which corresponds to an acoustic frequency of 600 Hz. Of course, these bubble sizes just described correspond to the large end of the spectrum; however, these larger bubbles are also much more efficient in radiating energy. The very densely populated bubble clouds generated by plunging breakers prevented us to accurately measure the bubble size distribution with the optical technique described earlier.

Figures 10(a)-(c) show the power density plots for weak spilling, moderate spilling and plunging breakers, respectively. The power densities shown in these figures were averaged over 100 samples. The weak breaker has a prominent peak at around 2 kHz [Fig. 10(a)]. This corresponds to a bubble size of approximately 1.65 mm in radius. The spectral slope of the noise from the weak breaker is roughly 6 dB/oct from 2 to 20 kHz and follows f-2. Increasing breaker severity entrains more air and produces larger bubbles. The histogram of the bubble size distributions of the weak breaker shows the existence of bubbles in the range of 1.65 mm. Larger bubbles, in general, radiate higher energies than the smaller ones and the overall energy of few larger bubbles may be greater than a large quantities of smaller bubbles. The power density of the moderate breaker shown in Fig. 10(b) clearly indicates a shift to lower frequencies. This fig-

1761 d. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 A.R. Kolaini and L. A. Crum' Observations of underwater sound 1761


1oo

g5

70

55

!

40[ , 0.1

i i i i i i i I i i i i i i • • i

1.0 I0 O

1oo

85

7o

55

40

0.1

i i i i , I i i I i i I i i i i I I

i i i i i ! i i I i i ! , i i i i !

1.0 10.0

lOO

85

7o

55

/•0 I I I I I I I I I I , I I , I

o.1 1.o 1o.o

Frequency (lcHz)

FIG. 10. Power densities averaged over 100 acoustic signals of (a) the weak spilling breakers with a peak at around 2 kHz; (b) the moderate spilling breakers with a peak at around 600 Hz. Note the existence of significant spectral components for frequencies as low as 100 Hz; (c) the weak plunging breakers with a peak at around 200 Hz. The solid lines are the best curve fit to the data. Note the shift from low intensities and high frequencies in (a) to the relatively high intensity and low frequencies in (c). The peaks near 550 and 950 are most likely due to modes in the tank. The peaks below 400 Hz are below the cutoff frequencies for the tank and may represent collective oscillations of bubble clouds formed by breakers.

ure has a broadband spectral peak with a maximum at around 600 Hz corresponding to a bubble size of 5.5 mm in radius. The spectral slope of this figure is roughly 5 dB/oct from 500 Hz to 12.5 kHz. This slope is close to that observed for wind-dependent ambient noise in the ocean (Knudsen et al., 1948), which follows f-l.5 behavior. Wenz (1962), also shows the same slope, wind-dependent spectra in the range of 50 Hz to 10 kHz; this slope rapidly decreases near 1 kHz, with a peak around 500 Hz. Finally, the shift in the spectral peak to about 200 Hz is evident in the power density shown in Fig. 10(c) for the plunging breaker. The significant broadband low-frequency noise generation below 200 Hz demonstrates that collective oscillations of a bubble cloud are possible with breaking waves. At the lower end of the spectrum, the collective oscillations appear to dominate over the single bubble pulsations.

The notion that low-frequency sound can be generated under breaking waves by collective bubble cloud oscillations was hypothesized independently by Carey and Browning (1988), and by Prosperetti (1988a,b). As was indicated earlier, the onset of collective oscillations may occur by large clockwise eddies containing various bubble sizes. The radius of the bubble cloud created by the large vorticity is measured

_

to be about 10 cm. The average void fraction,/•, in the cloud is also measured and is about 0.150. As a rough estimate, this cloud can be regarded as a system of coupled oscillators, which has a series of normal modes, the lowest one of which is given by

f •Cm12R, (1)

where C m is the sound speed inside the bubbly cloud, and R is the radius of the cloud. At frequencies much below the resonance frequency of the bubbles, damping effects can be neglected, and the sound speed as a function of void fraction

_

/• can be written (Prosperetti, 1988b),

(2)

With the value of the void fraction measured for a weak

plunging breaker and our estimate of the size of the cloud, we can calculate a velocity of sound (within the cloud) to be about 26 m/s. With this value of the sound speed, we see that the lowest normal mode of oscillation is estimated to be

around 130 Hz, which is consistent with measured values. There remains the question of why the frequency peaks

in the power density slots do not correspond (via the Min- naert formula) to the peaks in the measured bubble distribution functions. We believe that this discrepancy is due to nearest neighbor effects. It has been demonstrated (Strasberg, 1956; Gilbert and Wang, 1990; Prosperetti, 1994) that a single bubble, isolated from other bubbles, can resonate near its natural (Minnaert) frequency. However, when a second bubble of the same radius is placed a few radii away, the two bubbles resonate at a frequency approximately 10% lower. When three bubbles are considered, the frequency drops to 15% of this natural frequency. This progression continues until collective effects need to be considered. Thus although individual bubbles may be responsible for the majority of the

1762 J. Acoust. Soc. Am., Vol. 96, No. 3, September 1994 A.R. Kolaini and L. A. Crum' Observations of underwater sound 1762


radiated noise in weak to moderate breakers, the frequencies radiated are determined by the number, sizes, and distances of bubbles in their vicinity.

It is interesting to note there are repeatable peaks in the power density spectra for the various breakers shown in Fig. 10(a)-(c). In addition to an increase in dB levels over all frequencies with increasing breaker severity and approximately 5-6 dB/oct slopes, there may be nonlinear coupling between asymmetrical bubble oscillations and the volume pulsation as predicted by Longuet-Higgins (1990).

The acoustic energy radiated by breaking waves can be estimated by assuming plane traveling waves with particle velocities given by u = P/poc, where p is the acoustic pressure, and P0, c are the liquid density and sound velocity, respectively. The acoustic energy radiated by breaking waves can be estimated by assuming they act as a point source and the contribution of surface reflection can be accounted for by the method of images. The time-average intensity is, therefore, given by

• • ••a • ] =• • Pac dt cos 2 O, (3) I(r,O) poc Tac c where P ac is the acoustic radiated pressure measured, rac is the duration of the breaking wave acoustic "event," r is the distance between source and the receiver, and 0 is the angle subtended by r relative to the pressure release boundary. As- suming the dipole behavior of the noise source (Kennedy, 1992), the total radiated energy is obtained by integrating Eq. (3) over a hemisphere of radius R0 centered at the point where the dipole intersects the pressure release surface,

2rrR• Crac 2 ] II= 3poc Jo P•c dt. (4) Thus by measuring the rms acoustic pressure at a fixed point in the tank, it is possible to determine the total radiated energy flux.

Similarly, the surface displacement measurements were

used to estimate the wave energy E •'w' in a group of duration rw just prior to breaking,

1

E•w= 7poglcgrwr] 2, (5) where g is the gravity constant, ½g is the group velocity, rw is the sampling period of gravity waves, I is the tank width, and r/2 is the average square of the water surface.

Figure 11 is a plot of the average acoustic intensity measurements, as defined by Eq. (4), versus the total energy measured in the gravity wave group of duration rw prior to breaking, given by Eq. (5). The speed of sound in the liquid is taken to be constant with a value of 1480 m/s. The corre-

lation between radiated acoustic energy and wave energy prior to breaking may be useful in monitoring wave energy in the ocean. Note the existence of different slopes in the acoustic-gravity wave energy correlation curve. The change in the character of the data presented in Fig. 11 is analogous to the measurements in the ocean (Kennedy, 1992; Kerman, 1984). Kennedy's data show that the dipole source level has a different character above and below a critical friction ve-

locity of the wind. It is at this critical value that the ocean

. ,

3-

2

1

0 . , I , , , I , , , I , , , I , , , •

4 6 8 10 12

Energy of Gravity Waves (Joules)

FIG. 11. Correlation between the total acoustic radiated energy due to breaking with the total energy of the waves prior to breaking. The dramatic change in slope probably represents fundamentally different behavior and is likely associated with the transition from spilling to plunging breaker behavior.

surface changes from an aerodynamically smooth to a rough surface. The change in slopes shown in Fig. 11 may be in- terpreted as the transition between the relatively less energetic spilling breakers to high energetic plunging breakers. The ambient noise data acquired by Morris (1978) in the northeastern Pacific Ocean show similar trands. They have shown that the noise levels at frequencies from 100-800 Hz increase with increasing wind speeds above 7 knots. It is clear that with increasing wind speeds, both single bubbles as well as collective oscillation of bubbles may contribute to the sound pressure level, later of which is more dominant at higher wind speeds with more energetic waves. Results of laboratory measurements of breaking waves published by Loewen and Melville (1991) show correlation exist between the acoustic radiated energy and mechanical energy dissipated.

The radiation efficiency, defined as the ratio of the estimated acoustic energy [Eq. (4)] to the energy of the wave [Eq. (5)] can also be calculated (Carey et al., 1993). The result shows values ranging from 0.8X10 -7 to 1.09X10 -6 , depending upon the severity of the breaker. The acoustic efficiencies observed in this experiment is comparable to those expected in the sea with the occurrence of the white- caps.

III. CONCLUSIONS

We have examined the underwater noise radiated by breaking waves in a fresh water laboratory environment. By utilizing a computer controlled wavemaker and a large anechoic water tank, we were able to generate breakers of various types and intensities. From the analysis of high- speed cinephotography of breaking waves, and the associated sound generation, we have examined the physical sources of the noise produced by breaking waves. Our laboratory data suggests that the noise generated by the majority



of spilling breakers in fresh water is the result of newly created bubbles. Hydrodynamically, these bubbles are entrained by a turbulent flow field produced by shear across the inter- face and a vorticity field at the leading edge of the whitecap. These entrained bubbles are produced with excess surface and potential energy; they subsequently radiate this energy in the form of acoustic waves.

We observe a gradual transition from relatively low intensity, relatively high frequency acoustic emissions from gently spilling breakers to relatively high intensity, relatively low frequency emissions from plunging breakers. For the gentle spilling breakers, relatively small numbers of individual bubbles of relatively small size are produced. It appears as if the majority of sound is produced by these individual bubbles resonating at their natural frequencies. However, as the intensity of the breaker increases, more bubbles are produced. Although the size of the bubbles tends to get larger, they do not become large enough for the individual bubbles radiating alone to account for the full range of acoustic emissions observed. We interpret this behavior to result from the fact that individual bubbles are experiencing the influence of their nearest neighbors, and thus radiate at a lower frequency because of mass loading (Prosperetti, 1988a,b, 1994; Gilbert and Wang, 1990). As the breaking wave tends more and more toward a plunging breaker, the concentration of bubbles and the associated void fraction be-

comes relatively large, the hydrodynamics of the breaking process leads to the production of eddies, and the acoustic emissions extend to the very low frequencies (<200 Hz). It appears that, in this case, compact bubble clouds are radiating as a unit, in the form of collective oscillations.

These breaking waves have been produced in fresh water, which tends to entrain larger bubbles than similar-sized breakers produced in salt water. Accordingly, we can extend our laboratory results to the salt water case by assuming that similar behavior will occur, with the simple exception that there will be a generation of larger numbers of smaller bubbles.

These results also have implications concerning the origins of bubble related ambient noise in the ocean. We note that, when gentle spilling breakers are produced, the noise radiated is generated principally by individual bubbles radiating at their natural resonance frequencies. The hydrodynamics of the breaking wave process and the associated noise production tend to result in a 5 dB/oct falloff, with a frequency that is observed both in the laboratory and in the ocean (Knudsen et al., 1948; Wenz, 1962). As the intensity of the breaking wave increases or, in the open ocean case, as the wind speed increases, there is an associated increase in the magnitude of the acoustic radiation and a gradual shift to lower frequencies. Especially in the salt water case, the sizes of the bubbles entrained must remain relatively constant, and thus the shift to lower frequencies must result from the dynamic loading of individual bubbles by their nearest neighbors. Eventually, when extremely high sea states are encoun- tered, radiated acoustic frequencies extend to very low frequencies, even below 10 Hz. These frequencies can only be associated with the oscillation of large bubble clouds where the void fraction is sufficiently large to lead to ex-

tremely low effective-medium velocities. Our laboratory results thus produce a rational explanation for the origins of wind-dependent ambient noise in the ocean, from frequencies that range from in excess of 100 kHz to a few Hz.

ACKNOWLEDGMENTS

The authors would like to thank Jeff Kolodziejczak in assisting in the design and development of the hydraulically controlled wave maker, Andrea Prosperetti for many helpful discussions, Alex Ruxton for assisting in data acquisition and analysis, and Reza Ahmadian for assisting in the modal analysis of the anechoic tank. We acknowledge also the support of the Office of Naval Research.

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Observations of underwater sound from laboratory breaking waves and the implications concerning ambient noise in the ocean