Modeling low frequency scattering from small schools of fish

Abstract

A low-frequency scattering model for small to moderately sized fish schools has been developed. The model uses a mathematical formalism based upon the harmonic solution of sets of coupled differential equations, and incorporates a verified swimbladder scattering ‘‘kernel’’ for an individual fish. All orders of multiple scattering interactions between the fish are included, and the aggregate scattering field calculated by coherent summation. Application to ensembles of closely spaced fish indicates significant deviations from the returns expected when incoherent scattering is dominant. The peak target strength is reduced and the resonance frequency is shifted due to multiple scattering. The target strength also varies strongly with frequency as a result of interference effects. For widely dispersed ensembles, the model reproduces the results of incoherent scattering. For larger ensembles the model predicts target strength values near the main resonance which diminish sharply with depth. The effects of a school on the scattering of any single individual within it become greater as the school size increases. By reducing the viscous damping in the scattering kernel, the model can also describe scattering from small bubble clouds.