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. Threedimensional 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.

Compressibility effects on the structural evolution of transitional high-speed planar wakes

“…The constitutive shear layers of the wake act as a waveguide, as such, the perturbations within the wake are internally reflected, raising the possibility of the emergence of an acoustic instability modes as in the boundary layer (Mack 1975(Mack , 1990). Interestingly, the information which does exit the waveguide is preferentially inclined to the free stream with an increasing streamwise orientation with Mach number, recalling the findings of acoustic waves in the free stream by Watanabe & Maekawa (2004) and Maekawa, Takiguchi & Watanabe (2006). We recall that the acoustic intensity is proportional to the separation between two adjacent traces for an omnidirectional acoustic source (Papamoschou 1993): the closer two adjacent traces are to each other, the stronger the signal (valid under the assumption of zero wave dispersion or attenuation).…”