A new low-frequency scattering model for small to moderately sized fish schools has been developed. The model, which uses a mathematical formalism based upon the harmonic solution of sets of coupled differential equations, allows a verified swimbladder scattering ‘‘kernel’’ for the individual fish to be incorporated. It includes all orders of multiple scattering interactions between fish, and calculates the aggregate scattering field by coherent summation. Application to simulated ensembles of closely spaced fish indicates significant deviations from incoherent scattering returns. Peak target strength reductions, and shifts in the resonance frequency, appear due to multiple scattering. The target strength also varies strongly with frequency as a result of interference effects. When applied to widely dispersed ensembles, the model reproduces the results of incoherent scattering. For larger ensembles, at greater depth, the model predicts sharply reduced target strength values around the main resonance. The ensemble effects of a school on the scattering of any single individual show more fluctuations as the school size increases. By reducing the viscous damping in the scattering kernel, the model can also describe scattering from small bubble clouds. The model has been applied successfully to fit experimental broadband low-frequency scattering data from schooling fish.

A coupled oscillator method is used to describe collective acoustic resonances and scattering from multiple air bubbles in water. By recombining equations, the problem is decomposed into that of scattering from individual normal modes of the ensemble. Each mode has specific resonant properties. ‘‘Symmetric’’ modes, where the bubbles oscillate in phase with each other, typically show downward frequency shifts and increased damping. ‘‘Antisymmetric’’ modes, where some or all of the bubbles oscillate in antiphase, generally show upward frequency shifts and reduced damping. For two bubbles the method predicts frequency shifts which agree with experimental results. The resonance response functions predict that a two bubble system may become superresonant provided (a) the mode is antisymmetric, (b) the individual bubbles are primarily radiation damped, and (c) the bubbles are spaced such that the modal damping is small. Superresonant scattering is dipolar and propagates little energy in the far field, making the phenomenon difficult to observe experimentally. Scattering from a bubble reflected in a pressure release surface may show the phenomenon strongly. The antisymmetric modes of a triangular arrangement of three bubbles are degenerate and may also become superresonant. The damping of line ensembles of bubbles varies strongly with the bubble spacing.

Acoustic scattering from many species of fish is strongly increased by the resonance response of the swimbladder. This gas-filled, elastic-walled internal sac may have several functions, including hearing and buoyancy. A complete physical description of the response must include the swimbladder wall, the surrounding flesh, and the gas enclosed. This work presents a new mathematical/physical model to describe resonance scattering from swimbladder fish. The model consists of a spherical air bubble enclosed, first, by an elastic shell (representing the swimbladder wall), and then by a viscous shell (representing the surrounding fish flesh). The rigidity of the inner shell increases the monopole resonance frequency of the bubble. The viscosity of the outer shell causes the resonance to be damped. By allowing these factors to vary within physically reasonable bounds, the new model has been used to explain the experimentally measured resonance frequencies and damping of swimbladder resonances in Atlantic cod. The model provides insights into the physiological mechanisms by which fish may actively control the resonance frequencies of their swimbladders to improve hearing, and how this control can be lost under varying water pressure conditions. The impact of this issue on fisheries survey procedures is discussed.

The classic theory of linear acoustic propagation in bubbly water inaccurately represents the physical behavior of dense populations of resonating bubbles. It assumes the bubbles always oscillate independently, while they may actually be strongly coupled by acoustic radiation, especially when uniformly sized. Sound propagation can be properly understood only in terms of the collective action of the medium, which is dominated by the ‘‘symmetric’’ normal mode. In this work, the propagational characteristics of bubbly water are determined by averaging the ensemble behavior of the symmetric mode over distributions of bubble radii and locations. The method includes all orders of multiple scattering, and incorporates ‘‘shielding’’ effects in the medium. New theoretical expressions for the phase speed and attenuation are obtained, and compared to experimental data by integrating multiple scattering effects over a ‘‘region of collective interaction’’ around each bubble. For uniform bubbles and volume fractions β ≥ 0.22%, multiple scattering strongly influences propagation. When β < 0.22%, the effects apparently diminish sharply. For nonuniform bubbles and β ≊ 0.02%, multiple scattering effects are not indicated. These results imply that the classic theory should provide an adequate description of the acoustic properties of bubble plumes and clouds typically encountered in the ocean.

A T-matrix expansion technique has been used to investigate the monopole acoustical resonances of bubbles deformed into elongated axisymmetric objects (specifically: prolate spheroids and cylinders with hemispherical endcaps). The bubbles are modeled as air-filled inclusions in water. Scattering occurs because of the change of acoustical impedance at the interface between the two media. The results confirm that the resonance frequency of a bubble increases when it is deformed from a spherical shape. It increases more quickly with aspect ratio for cylindrical than for prolate spheroidal bubbles. The resonance frequency is also independent of the direction of excitation. For both cylindrical and prolate spheroidal bubbles the frequency width of the resonance increases with the deformation; but the corresponding values of Q fall more quickly for the cylindrical bubble. The scattering amplitude also decreases with the deformation, especially for endfire incidence. The angular distribution of acoustic scattering changes with the shape of the bubble. For spheroidal bubbles there is relatively little change from the spherical pattern obtained with an undeformed bubble; but for cylindrical bubbles the scattering may be irregular, with pronounced lobes in the broadside direction.