On the origin of streamwise vortices in braid regions for compressible mixing layers

Abstract

The origin of initial streamwise vortices in braid regions and their relationship with deformed spanwise vortices are numerically studied via direct numerical simulation (DNS) in the compressible mixing layer with a convective Mach number (Mc) of 0.4. Through an analysis of fast Fourier transform on DNS data, two low-rank velocity models (vd and vs) are developed to demonstrate that both deformed spanwise vortices and streamwise vortices are all originated from the linear superposition of a fundamental norm mode [mode (1, 0)], a pair of fundamental oblique modes [modes (1, ±1)], and a mean mode. Further investigations reveal that, downstream of spanwise vortices, the increase in amplitude ratio (Ao/An) between modes (1, ±1) and mode (1, 0) leads to the formation of deformed spanwise vortices in vortex regions. As the amplitude ratio Ao/An further increases, reaching the threshold that the streamwise rotation motion from modes (1, ±1) exceeds the spanwise irrotational deformation from mode (1, 0), streamwise vortices are generated in braid regions. The aforementioned formation path for deformed spanwise vortices and streamwise vortices provides a mechanism support for our flow visualization results that the emergence of deformed spanwise vortices precedes that of streamwise vortices in the flow field.