A viscous-elastic swimbladder model for describing enhanced-frequency resonance scattering from fish

Acoustic scattering from many species of fish is strongly increased by the resonance response of the swimbladder. This gas-filled, elastic-walled internal sac may have several functions, including hearing and buoyancy. A complete physical description of the response must include the swimbladder wall, the surrounding flesh, and the gas enclosed. This work presents a new mathematical/physical model to describe resonance scattering from swimbladder fish. The model consists of a spherical air bubble enclosed, first, by an elastic shell (representing the swimbladder wall), and then by a viscous shell (representing the surrounding fish flesh). The rigidity of the inner shell increases the monopole resonance frequency of the bubble. The viscosity of the outer shell causes the resonance to be damped. By allowing these factors to vary within physically reasonable bounds, the new model has been used to explain the experimentally measured resonance frequencies and damping of swimbladder resonances in Atlantic cod. The model provides insights into the physiological mechanisms by which fish may actively control the resonance frequencies of their swimbladders to improve hearing, and how this control can be lost under varying water pressure conditions. The impact of this issue on fisheries survey procedures is discussed.