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

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 (v(d) and v(s)) 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 (A(o)/A(n)) between modes (1, +/- 1) and mode (1, 0) leads to the formation of deformed spanwise vortices in vortex regions. As the amplitude ratio A(o)/A(n) 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. Published under an exclusive license by AIP Publishing.

Automated summary

The origin and relationship between initial streamwise vortices in braid regions and deformed spanwise vortices are studied using direct numerical simulation (DNS) in a compressible mixing layer. Through analysis of DNS data using fast Fourier transform, two low-rank velocity models (v(d) and v(s)) are developed to show that both deformed spanwise vortices and streamwise vortices originate from the linear superposition of several modes. Further investigations reveal that the increase in amplitude ratio between modes leads to the formation of deformed spanwise vortices in vortex regions and the generation of streamwise vortices in braid regions.