Sound produced by a vortex interacting with a cavitated wake

Abstract

A linearized analysis is made of the canonical problem of sound production during the convection of a line vortex of strength $\Gamma$ in steady flow of water over a ‘fence’ of height $h$ on a flat wall in the presence of a vacuous cavity in the wake of the fence. The cavity is assumed to extend sufficiently far downstream for sound waves to be regarded as launched above a non-compact, pressure-release surface. Additional vorticity is released from the tip of the fence in accordance with the Kutta condition, and is convected at the mean stream speed $U$ along the free streamline boundary of the cavity. Sound pressures of opposite phases are generated by the incident and the shed vorticity. The predicted radiation consists of a pressure pulse of amplitude proportional to $\rho_oU\Gamma/h$ ($\rho_o$ being the mean water density) and width approximately equal to fence height/mean flow Mach number, produced as the vortex passes the tip of the fence. The acoustic amplitude decreases rapidly at later times because of destructive interference between the sound generated by the impinging vortex and the shed vorticity.