Interfaces of high- and low-speed large-scale structures in compressible turbulent mixing layers: compressibility effects and structures

Abstract

Direct numerical simulations of temporally developing mixing layers have been performed to investigate the effects of compressibility on statistics and structures near the interfaces of high- and low-speed large-scale structures (LSSs), covering a range of convective Mach numbers from $M_c=0.2$ to $1.8$ and Taylor Reynolds numbers up to 290. The interfaces of LSSs are directly defined by the isosurface of zero fluctuating streamwise velocity. The characteristic velocity jump at the interfaces grows rapidly in the transition stage and then decreases until reaching a gradual self-similar stage. The evolution of velocity jump is evidently delayed as the convective Mach number increases. The interface layer is formed by the shearing motion of neighbouring LSSs. A small vortical motion characterized by the Kolmogorov scale is induced in the interface layer by shear-dominated outer regions. The strengths of outer shearing motion and central vortical motion are greater at the leading edge, but smaller at the trailing edge, which is also reflected in a larger velocity jump at the leading edge. As the convective Mach number increases, the small-scale vortical structure is obviously suppressed by compressibility. At high convective Mach number $M_c=1.8$ , the compressive shear-dominated outer regions are linked with a sheet-like structure passing through the centre of the expansion region corresponding to a small-scale vortical structure. The compressibility and shearing strength near the interface are highly dependent on the interface orientation.