Laboratory measurements of the sound generated by breaking waves
Loewen, Mark Richard
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Breaking waves dissipate energy, transfer momentum from the wind to surface currents and breaking enhances the transfer of gas and mass across the air-sea interface. Breaking waves are believed to be the dominant source of sea surface sound at frequencies greater than 500 Hz and the presence of breaking waves on the ocean surface has been shown to enhance the scattering of microwave radiation. Previous studies have shown that breaking waves can be detected by measuring the microwave backscatter and acoustic radiation from breaking waves. However, these techniques have not yet proven effective for studying the dynamics of breaking. The primary motivation for the research presented in this thesis was to determine whether measurements of the sound generated by breaking waves could be used to quantitatively study the dynamics of the breaking process. Laboratory measurements of the microwave backscatter and acoustic radiation from two-dimensional breaking waves are described in Chapter 2. The major findings of this Chapter are: 1) the mean square acoustic pressure and backscattered microwave power correlate with the wave slope and dissipation for waves of moderate slope, 2) the mean square acoustic pressure and backscattered microwave power correlate strongly with each other, and 3) the amount of acoustic energy radiated by an individual breaking event scaled with the amount of mechanical energy dissipated by breaking. The observed correlations with the mean square acoustic pressure are only relevant for frequencies greater than 2200 Hz because lower frequencies were below the first acoustic cut-off frequency of the wave channel. In order to study the lower frequency sound generated by breaking waves another series of two-dimensional breaking experiments was conducted. Sound at frequencies as low as 20 Hz was observed and the mean square acoustic pressure in the frequency band from 20 Hz-l kHz correlated strongly with the wave slope and dissipation. A characteristic low frequency signal was observed immediately following the impact of the plunging wave crest. The origin of this low frequency signal was found to be the pulsating cylinders of air which are entrained by the plunging waves. The pulsation frequency correlated with both the wave slope and dissipation. Following the characteristic constant frequency signal, approximately 0.25 s after the initial impact of the plunging crest, another low frequency signal was typically observed. These signals were generally lower in frequency initially and then increased in frequency as time progressed. To determine if three-dimensional effects were important in the sound generation process and to measure the sound beneath larger breaking waves a series of experiments was conducted in a large multi-paddle wave basin. Three-dimensional breaking waves were generated and the sound produced by breaking was measured in the frequency range from 10 Hz to 20 kHz. The observed sound spectra showed significant increases in level across the entire bandwidth from 10 Hz to 20 kHz and the spectra sloped at -5 to-6 dB per octave at frequencies greater than 1 kHz. The mean square acoustic pressure in the frequency band from 10 Hz to 150 Hz correlated with the wave amplitude similar to the results obtained in the two-dimensional breaking experiments. Large amplitude low frequency spectral peaks were observed approximately 0.75 s after the initial impact of the plunging crests. It was postulated that the low frequency signals observed some time after the initial impact of the plunging crests for both the two and three-dimensional breakers were caused by the collective oscillation of bubble clouds. Void fraction measurements taken by Eric Lamarre were available for five breaking events and therefore the average sound speed inside the bubble clouds and their radii were known. Using this information the resonant frequencies of a two-dimensional cylindrical bubble cloud of equal radius and sound speed were calculated. The frequencies of the observed signals matched closely with the calculated resonant frequencies of the first and second mode of the two-dimensional cylindrical bubble cloud. The close agreement supports the hypothesis that the low frequency signals were produced by the collective oscillation of bubble clouds. In Chapter 4 a model of the sound produced by breaking waves is presented which uses the sound radiated by a single bubble oscillating at its linear resonant frequency and the bubble size distribution to estimate the sound spectrum. The model generates a damped sinusiodal pulse for every bubble formed, as calculated from the bubble size distribution. If the range to the receiver is known then the only unknown parameters are ε, the initial fractional amplitude of the bubble oscillation and L, the dipole moment arm or twice the depth of the bubble below the free surface. It was found that if the product εxL is independent of the bubble radius the model reproduces the shape and magnitude of the observed sound spectrum accurately. The success of the model implies that it may be possible to calculate the bubble size distribution from the sound spectrum. The model was validated using data from experiments where the breaking events were small scale gently spilling waves (Medwin and Daniel, 1990).
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution December 1991