Acoustic Wave Generation in a Compressible Wake

Abstract

The compressible Navier-Stokes equations are numerically solved to study the acoustic generation mechanism associated with the evolution of the structure in a compressible plane wake undergoing transition to turbulence. High-order compact finite difference schemes are used for spatial derivatives and a 4th-order Runge-Kutta scheme is employed for time advancement. Navier-Stokes characteristic boundary conditions are used in the vertical direction and periodic boundary conditions in the streamwise and spanwise directions. Three-dimensional structures of the wake are studied by means of temporally evolving plane wakes forced with a combination of unstable modes obtained from linear stability theory using a mapped Fourier method for the viscous compressible equations. Forcing with a pair of oblique subharmonic unstable modes yields streamwise/vertical counter- rotating vortices in the saddle region. As the streamwise/vertical vortices evolve outside, their self-induction causes inclined braidlike structures to form in the wake, which are similar to observations in the experimental supersonic flat wake transition. The oblique subharmonic unstable modes also cause the spanwise variations in the core that lead to roller distortion. Acoustic waves of plane wakes are generated when two-dimensional rollup structures appear and rotate in such wakes. Near-field sound wave pressure decreases downstream due to the three-dimensional evolution of the wake.