Analysis of acoustic scattering from large fish schools using Bloch wave formalism
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In the open ocean acoustic scattering by SONAR sources can be dominated by large fish schools. Multiple scattering effects are strong and the individual fish air-filled swimbladders scatter in the 1-10 kHz frequency range for most fish sizes. Furthermore, these schools are typically large in comparison to the acoustic wavelength and the individual fish typically swim in nearly periodic arrangements with a separation distance of approximately one body length. Hence, this work takes the perspective that fish schools can be studied simply and effectively by invoking the formalism of Bloch waves in periodic media. Analysis of the periodic school is aided through the Bloch theorem which reduces the study of the entire school to the study of a unit cell containing a single fish swimbladder. Application of the Bloch formalism to the school requires study of acoustic reflection from a semi-infinite half-space composed of an infinite tessellation of air-filled swimbladders in water. This media is denoted a fluid phononic crystal (PC). The reflection is considered, using a finite element discretization of the unit cell and an expansion of Bloch waves for the transmitted wave field. Next, scattering from a large finite school is studied through the context of the Helmholtz-Kirchhoff integral theorem where the semi-infinite PC pressure, determined by the Bloch wave expansion, is used as the surface pressure. Validation of results is accomplished via comparison with a finite element model (two dimensions) and a low frequency analytical multiple scattering model (three dimensions). Analysis of the dispersion relationship of the infinite PC yields useful information for a large school, namely, the frequency corresponding to target strength peaks, even as wave incidence angles and internal fish spacing are varied. The scattering effects attributed to the shape and weak internal disorder of the finite school were investigated with the surface integral method and a perturbation scheme. A general model using Bloch formalism, that encompasses the internal fish structure, fish biologic properties, and realistic school effects such as varying school geometry and disorder, was formulated. Transient analysis of the frequency dependent scattering, using the proposed approach developed in this thesis, may assist SONAR operators better classify large fish schools based on the observed characteristics of the scattered field.