Linear stability analysis on supersonic streamwise vortices

In this study, the spatial growth rates of supersonic streamwise vortices were investigated by inviscid linear stability analysis. The freestream Mach numbers were 2.5, 5.0, and 7.5. In previous measurements taken to define the streamwise vortices, the stagnation temperature profile of supersonic flows is approximately uniform. This study found that the growth rate of vortices at the uniform stagnation temperature is smaller than that of isentropic vortices. The instability properties of the streamwise vortices can be explained by the ratio of the circulation to the axial velocity deficit, and also by the Mach number. Moreover, it is found that the compressibility effect, by which the instability reduces as the Mach number increases, is caused by the negative energy arising from the entropy gradient of supersonic vortices that accompanies the axial velocity deficit-like wake. From an energy perspective, the effect may reasonably be correlated with the large density perturbations in supersonic flows. This study also proposes a general convective Mach number for supersonic streamwise vortices. The normalized growth rates are shown to be a function of convective Mach number within the investigated range of ratio parameters.