Two-dimensional large-scale structures in a compressible shear layer

The effect of compressibility on the two-dimensional large-scale structures in a single shear layer was investigated for the temporally developing case. Each eddy is elongated by compressibility through (i) the formation of volumetric source and sink distribution and (ii) the emergence of unstable travelling waves under the condition that the Mach number of free streams, M, exceeds unity. The dilatation accelerates the streamwise velocity and decelerates the transverse velocity, so that the convection of vorticity makes the resulting eddy elongated in the streamwise direction and reduces its own angular velocity of rigid-body rotation. The eddy formed at M>1 takes an airfoil-like shape and has almost the same thickness as the original shear layer, due to an existing phase velocity different from the mean value of the two free stream velocities. Each eddy can propagate by itself in such a way that its leading edge rolls up the tail of the preceding eddy.