Recent work has rendered possible the formulation of a rigorous model for the propagation of pressure waves in bubbly liquids. The derivation of this model is reviewed heuristically, and the predictions for the small-amplitude case are compared with the data sets of several investigators. The data concern the phase speed, attenuation, and transmission coefficient through a layer of bubbly liquid. It is found that the model works very well up to volume fractions of 1%–2% provided that bubble resonances play a negligible role. Such is the case in a mixture of many bubble sizes or, when only one or a few sizes are present, away from the resonant frequency regions for these sizes. In the presence of resonance effects, the accuracy of the model is severely impaired. Possible reasons for the failure of the model in this case are discussed.

The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p0(R0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is presented in which the internal pressure is obtained numerically and the polytropic approximation is no longer required. Several comparisons are given of the two formulations, which describe in some detail the limitations of the polytropic approximation.

A high-frequency acoustic experiment was performed at a site 2 km from shore on the Florida Panhandle near Fort Walton Beach in water of 18-19 m depth. The goal of the experiment was, for high-frequency acoustic fields (mostly in the 10-300-kHz range), to quantify backscattering from the seafloor sediment, penetration into the sediment, and propagation within the sediment. In addition, spheres and other objects were used to gather data on acoustic detection of buried objects. The high-frequency acoustic interaction with the medium sand sediment was investigated at grazing angles both above and below the critical angle of about 30 . Detailed characterizations of the upper seafloor physical properties were made to aid in quantifying the acoustic interaction with the seafloor. Biological processes within the seabed and the water column were also investigated with the goal of understanding their impact on acoustic properties. This paper summarizes the topics that motivated the experiment, outlines the scope of the measurements done, and presents preliminary acoustics results. A preliminary summary of the meteorological, oceanographic, and seafloor conditions found during the experiment is given by Richardson et al. [1].

The bubble population near the ocean surface is of considerable interest. This population affects surface scattering strength, propagation near the surface, and the exchange of gases between the atmosphere and the sea. Both optical and acoustical means have been used to measure the bubble population with varying degrees of success. The acoustic method requires measurements at multiple frequencies and their subsequent conversion to bubble densities through either the resonance theory approximation or numerical solution of the resulting integral equation. In this paper, a numerical solution to the integral equation is obtained using the method of weighted residuals with linear B splines as basis functions. A regularization technique is employed to stabilize the solution. A number of plausible bubble distribution functions are generated along with their acoustic properties to test the robustness of the technique. This approach is shown to yield very accurate bubble distributions from highquality attenuation data.

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Comparisons of experimental optical and acoustical bubble size spectra disagree in size distribution at the low end of the spectrum. Previous methods of obtaining acoustic bubble size information relied strictly on resonant acoustical scattering and absorption theory. For some plausible distributions, these traditional methods greatly overpredict the number of bubbles present in a volume of fluid for bubble radii of 50 μ or less. Two cases are investigated that show the magnitude of departure from a priori bubble size distributions and are used to benchmark traditional acoustical scattering and absorption-based methods for obtaining spectra. A third possible bubble distribution is presented that is consistent with resonant approximation theory; however, the acoustic properties of this distribution are inconsistent with measurements from naturally occurring bubble populations. It is argued that off-resonance contributions to acoustical bubble spectra determinations need to be included.

The determination of acoustic scattering from a rough sea surface has received considerable attention in recent years. Knowledge of whitecap characteristics [J. Wu, IEEE J. Oceanic Eng. 17, 150–158 (1992)] has led to a better understanding of surface scattering phenomena [D. F. McCammon and S. T. McDaniel, IEEE J. Oceanic Eng. 15, 95–100 (1990)]. For this study a substantial amount of backscattering data was acquired with autonomous underwater vehicles running between 50 and 100 ft of the surface. These vehicles used a short pulse length sonar operating at 215 kHz. The use of a high-frequency sonar allows deep penetration of densely populated bubble plumes. Because of the high repetition rate, good spatial variation of backscattering strength from breaking waves has been obtained. Previous measurements by other scientists of bubble distribution functions in breaking waves allows an approximate conversion of scattering strength at the sonar frequency to most frequencies of interest. The database here consists of measurements made in deep water environments with seas ranging from sea state 0 to 3. The spatial variation of scattering strength due to the sea surface and bubble plumes from breaking waves is discussed as a function of wind speed.

ABST~ACT tions in the surface and subsurface layers of the are of considerable importance in physical Both optical and acoustical means have been ectrum when using acoustic resonant ethods for some bubble distributions of f bubble distribution functions that may be ocean is examined using both resonant nant scattering formalisms. Limitations of approximations are discussed for each bubble . The variation of density estimation error n to the next is explained using both ing cross section curves. A methodology he more accurate means of estimating bubble resonant theory (i.e. scattering or attenuation scussed. This methodology is intended to stic measurements for determining d in designing acoustic devices that rely of bubble densities. Finally, an outline of e bubble distribution calculations is ct distribution of air bubble sizes in interest to underwater acousticians, vices that rely on underwater acoustic sensors, o require correct bubble size distribution tical and electromagnetic remote sensors. The methods for obtaining data used to calculate utions lead to considerable disagreement over the they predict. The methods, optical bubble stic scattering and extinction measurements, used by numerous investigators. The data obtained ious investigators and the stated discrepancies are by MacIntyre' and Wu2. In attempting to e nature of the discrepancies between the optical methods, Commander and Moritz3 explored the bubble-resonance approximations measured acoustic data to size . We have shown that, while the resonance n for calculating attenuations and scattering (and riving bubble size distributions from such valid for some possible underlying (such as power law distributions), the resonance ch is by no means universal. 11s1In an earlier paper (ref.3), we showed that the resonance approximation is satisfactory if the underlying bubble distribution is a power law of the form Y e @ ) = Yoa-3.7, where a is the bubble radius. However, if the underlying distributions take different forms, such as a Gaussian distribution Y&u) = Y0e-c4-ry'z' or an exponential distribution, the resonance approximation fails to provide accurate results in the small size end of the spectrum. Since observed bubble populations in the ocean do appear to follow size distribution trends somewhere between the exponential and Gaussian distributions, a more robust approach is required. In reference 3 the need to include off-resonance contributions in calculating the acoustical bubble spectra is discussed and the method of doing so is outlined. 15In this paper a short review of the underlying physics and the resonance approximation is provided. Also included is an alternate method for examining the discrepancies between the exact theory and the resonance approximation approach. The paper concludes by providing more details on the means with which to solve the bubble size determination problem more accurately. The nature of the difficulties here resides in solving the inverse problem which in this case is a Fredholm integral equation of the first kind...