The Sound Generated by a Two-Dimensional Shear Layer: The Far Field Directivity from Computations and Acoustic Analogies

Abstract

The sound generated by vortex pairing in a two- dimensional mixing layer is studied by direct numerical simulation of the Navier-Stokes equations (DNS) for the layer and a portion of its acoustic field, and by solving Lilley's equation (with source terms determined from the DNS) for the entire acoustic field. Predictions for the acoustic field based on Lilley's equation are in good agreement with the DNS results. The radiated acoustic field at the pairing frequencies is highly directive and cannot be produced by point quadrupole sources. Instead, it is of the superdirective character considered by Crighton and Huerre (1990, J. Fluid Mech., 220), where the magnitude of the pressure varies like the exponential of the cosine of the angle between the observation point and the downstream axis. By making modifications to this basic directivity, we account, in part, for shear in the mean velocity and the convection of the acoustic waves by the different freestream velocities on either side of the layer, and obtain a good overall agreement between the theory and the computations.