A low-frequency acoustic scattering model for small schools of fish

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.