Resonance scattering by fish schools: A comparison of two models

The effective medium method is used to investigate resonance scattering from schools of fish with gas-filled swim bladders, as a function of frequency and azimuth. Calculations are also performed with a coupled differential equation model, which incorporates both multiple scattering between fish and wave interference interactions of their scattered fields [Feuillade, Nero, and Love, J. Acoust. Soc. Am. 99, 196–208 (1996)]. A theoretical comparison of the models for idealized spherical schools shows good agreement over the entire resonance region in the forward direction, where interference interactions have a minimal effect. Good agreement is also seen in back scattering at low frequencies, where the wavelength λ≥4s, and s is the average nearest neighbor fish separation. If λ<4s, the models diverge in back scattering, and the effective medium method fails. This can be critically important when migrations of schools to deeper water cause the collective resonance frequency to increase. Multiple scattering interactions are negligible when |4πnfb2/k|⪅0.01, where n is the fish number density, fb is the individual fish scattering amplitude, and k=2π/λ. A comparison with forward scattering data shows very good agreement for both models, and indicates a method for estimating fish abundance. For back scattering data, the effective medium method diverges strongly when λ<4s.