Analysis of Acoustic Scattering from Large Fish Schools Using Bloch Wave Formalism

date December 3, 2014
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Wednesday, December 3, 2014 4:00 p.m. ARL A009

Jason A. Kulpe
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology

In the open ocean, acoustic scattering of SONAR signals in the 1-10 kHz frequency range is dominated by large fish schools, where multiple scattering effects between the air-filled swim-bladders of the fishes within the school are strong. These schools are typically large in comparison to the acoustic wavelength and the fish typically swim in nearly-periodic arrangements with a separation distance of approximately one body length. Hence, the fish school 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’s swim-bladder. Application of the Bloch formalism to the school requires study of acoustic reflection from a semi-infinite half-space composed of an infinite arrangement of air swim bladders in water; this media is denoted a fluid phononic crystal (PC). The reflection is considered, using a finite element discretization of the unit cell, via 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 integral’s inputs. A general model using the Bloch formalism and encompasses the internal fish structure, fish biologic properties, and realistic school effects such as varying school geometry and disorder, will be explored. Transient analysis of the frequency dependent scattering, using the proposed model, may assist SONAR operators to better classify large fish schools based on the observed characteristics of the scattered field. Comparison of results is accomplished through a finite element model (two dimensions) and a low frequency analytical multiple scattering model (three dimensions).