Prediction of interface wave profiles for a flow‐excited cavity resonator

Abstract

Experimental and theoretical results are presented for a wall‐mounted cavity in turbulent flow, oscillating at Helmholtz or depth mode resonance. Data for interface waves at the mouth of the cavity, obtained by the CASH method, can be fitted to limiting expressions obtained from linearized instability theory. At typical steady‐state amplitudes, the wavelength of the disturbance agrees well with the predictions of Michalke [A. Michalke, J. Fluid Mech. 23, 521–544 (1965)], using an equivalent laminar flow model based on the mean velocity profile. Simple exponential growth of the driven wave does not occur, however, on account of nonlinear effects. Near the leading edge, the interface displacement is a superposition of a traveling wave and a stationary acoustic contribution. For the portion of the profile near the trailing edge, the traveling wave becomes predominant. Theoretical interface profiles have been used successfully in a root‐locus solution of the resonant frequency lock‐in problem, making it possible to predict Strouhal number and amplitude of cavity oscillation. [Work supported by a GHR contract with the Naval Ship Systems Command, administered by the Naval Ship Research & Development Center, Carderock, MD.]