Whistling of a deep axisymmetric cavity: interactions between an azimuthal aeroacoustic mode and the mean flow.*

Our experimental, numerical and theoretical study deals with the whistling of a deep axisymmetric cavity in a cylindrical duct subject to a low Mach turbulent flow. The aeroacoustic instabilities result from the constructive feedback between one of the trapped acoustic modes of the cavity and the dynamics of the shear layer at the cavity opening. Acoustic measurements reveal that the predominant instabilities involve the first azimuthal acoustic mode. For the first time in such configuration, time-resolved stereoscopic particle image velocimetry (PIV) is performed to visualize the three components of the velocity field in a two-dimensional cut of the cavity. The velocity fluctuations are then phase averaged to unravel the structure of the different hydrodynamic modes that contribute to the instabilities. The experiments allow us to discover a spontaneous symmetry breaking of the mean flow when a self-sustained high-amplitude aeroacoustic wave steadily spin around the cavity. It manifest itself by a mean swirling motion which predominantly rotates against the spinning direction of the wave. With a second order perturbation model on the Navier-Stokes equations, we show that the emergence of this mean swirl is caused by the Reynolds stress tensors arising from the hydrodynamic part of the aeroacoustic wave.