Accelerated Acoustic Boundary Element Method and the Noise Generation of an Idealized School of Fish

A transient, two-dimensional acoustic boundary element solver is developed using double-layer potentials accelerated by the fast multiple method for application to multibody, external field problems. The formulation is validated numerically against canonical radiation and scattering configurations of single and multiple bodies, and special attention is given to assessing model error. The acoustic framework is applied to model the vortex sound generation of schooling fish encountering 2S and 2P classes of vortex streets. Vortex streets of fixed identity are moved rectilinearly in a quiescent fluid past representative schools of two-dimensional fish, which are composed of four stationary NACA0012 airfoils arranged in a diamond pattern. The induced velocity on the fish-like bodies determines the time-dependent input boundary condition for the acoustic method to compute the sound observed in the acoustic far field. The resulting vortex noise is examined as a function of Strouhal number, where a maximum acoustic intensity is found for \(St \approx 0.2\), and an acoustic intensity plateau is observed for swimmers in the range of \(0.3< St < 0.4\). In the absence of background mean flow effects, numerical results further suggest that the value of Strouhal number can shift the acoustic directivity of an idealized school in a vortex wake to radiate noise in either upstream or downstream directions, which may have implications for the the study of predator-prey acoustic field interactions and the design of quiet bio-inspired underwater devices.