The compressible mixing layer: an LES study

This article employs LES to simulate temporal mixing layers with Mach numbers ranging from M _c  = 0.3 to M _c  = 1.2. A form of approximate deconvolution together with a dynamic Smagorinsky subgrid model are employed as subgrid models. A large computational domain is used along with relatively good resolution. The LES results regarding growth rate, turbulence levels, turbulence anisotropy, and pressure–strain correlation show excellent agreement with those available from previous experimental and DNS results of the same flow configuration, underlining the effectiveness and accuracy of properly conducted LES. Coherent structures during the transitional stage change from spanwise aligned rollers to streamwise-aligned thinner vortices at high Mach number. In the quasi-self-similar turbulent stage, the resolved-scale vorticity is more isotropic at higher M _c , and its vertical correlation length scale is smaller. The ratio of the vertical integral length scale of streamwise velocity fluctuation to a characteristic isotropic estimate is found to decrease with increasing M _c . Thus, compressibility leads to increased spatial decorrelation of turbulence which is one reason for the reduction in pressure–strain correlation with increasing M _c . The balance of the resolved-scale fluctuating vorticity is examined, and it is observed that the linear production by mean shear becomes less important compared to nonlinear vortex stretching at high M _c . A spectral decomposition of the pressure fluctuations into low- and intermediate-to-high-wave numbers is performed. The low-wave number part of the pressure field is found not to correlate with the strain field, although it does have a significant contribution to the r.m.s of the fluctuating pressure. As a consequence, the pressure–strain correlation can be analyzed using a simplified Green’s function for the Poisson equation as is demonstrated here using the LES data.