Stratified Kelvin-Helmholtz turbulence of compressible shear flows

We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin-Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16384(2)) and three-dimensional (with a spatial resolution of 512(3)) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k(-5/3) inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k(-5/3) scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k(-5/3) scaling. This difference may be assumed to be a reason for the k(-7/3) scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k(-3) scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k(-3) scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k(-2) for a larger compressibility parameter.