Three-dimensional evolution of structure and acoustic wave generation in a compressible plane wake

The compressible Navier-Stokes equations are numerically solved to study three-dimensional structures of a compressible plane wake undergoing transition to turbulence. High-order compact finite difference schemes are used for spatial derivatives and a fourth-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. Unstable disturbances are obtained from linear stability theory using a mapped Fourier method for the viscous compressible equations. Three-dimensional structures of the wake are studied by means of temporally evolving plane wakes forced with random disturbances and a combination of unstable modes. Forcing with a pair of oblique 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. The effect of the oblique unstable modes is also to cause the spanwise roller breakdown. Acoustic waves of the plane wake are generated when roughly two-dimensional rollup structures appear and rotate in the wake. The three-dimensional evolution of the wake reduces the near-field sound pressure.