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

Abstract

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.

Further insight into the sound-producing mechanism of clownfishes: what structure is involved in sound radiation?

“…This notion was supported by Feuillade and Nero (Feuillade and Nero, 1998), who showed that the presence of an elastic shell (representing the swimbladder wall) enclosed by a viscous shell (representing the surrounding fish tissue) induces a shift in resonance to a higher frequency.…”

Wall structure and material properties cause viscous damping of swimbladder sounds in the oyster toadfishOpsanus tau

“…Physiology and sound properties [16,17,28] fail to support classic notions that the oyster toadfish swimbladder behaves as either an underwater resonant bubble [14,15] or as a bubble contained by an isotropic, homogeneous, elastic rubber membrane [33], both of which would produce an rspb.royalsocietypublishing.org Proc. R. Soc.…”

“…Acousticians working on swimbladder scattering have tended to discount the swimbladder wall as a factor [29,30], and ascribed rapid decay to damping by surrounding fish tissue [31,32]. One complex mathematical treatment of codfish, modelled the swimbladder as an elastic rubber membrane surrounding an underwater bubble; the bladder in turn was assumed to be surrounded by viscoelastic fish tissue [33]. However, the model required parameter fitting in order to match results on live fish in a Norwegian fjord [34].…”

Depth-dependent target strengths of gadoids by the boundary-element method

“…The degree to which the fish controls the surface tension on the swimbladder wall may be significant, thus potentially affecting the target strength. 13,14 Notwithstanding these comments, the depth dependence of target strength from swimbladdered fish lacking rete mirabile seems clear: Boyle's law, or the inverse relationship of ambient pressure and volume, is operative. The mass of gas in the swimbladder is constant, and the swimbladder volume diminishes with depth, affecting the target strength.…”