Coherent structures in the transition of compressible planar wakes

Temporally evolving direct numerical simulations of transitioning plane wakes are conducted to study the influence of compressibility on the developed structures in the flow. Four cases are investigated with free stream Mach numbers of 0.3, 0.8 1.2 and 2.0. The growth rate of the inviscid linear stability approximation collapses the turbulence statistics in the linear region of the flow for the low compressible cases. At higher Mach, the scaling does not provide as good of an agreement. The investigation of the preferential wavelengths reveals an increased three-dimensionality with Mach number, a result that is supported by experimental observations but contradicts the linear stability results. We attribute the increased three-dimensionality to the receptivity of the wake to the symmetric (varicose) mode. The varicose mode is two-dimensional at low Mach number but becomes oblique in the supersonic regime. In opposition to the mixing layer, the high-speed wake undergoes a spreading rate increase with increased Mach number during transition, despite a reduced linear growth rate. As the principal instability wavelength increases with compressibility, the developed rollers are larger with a higher circulation. The pairing of these structures results in a stronger cross wake momentum transfer and consequently, an increased lateral spreading. In addition, the instantaneous visualization of the braided structures reveals an increased streamwise alignment with increasing compressibility.