Nonlinear stability and vortex structure in spatially developing mixing layers with PSE method

The method of nonlinear parabolized stability equations (PSE) is applied in the simulation of nonlinear development of stability waves and the vortex structures in supersonic mixing layers. The PSE method decomposes the disturbances into a rapidly wave-like part and slow-varying shape function. The nonlinear development of disturbance in supersonic mixing layers are modeled using spatial marching method, which makes the computational costs much smaller than that of traditional large scale simulation methods such as DNS and LES. Vortex structures in supersonic mixing layers are simulated, such as vortex roll-up, vortex pairing, and Λ vortex exited in different types of disturbances. The results demonstrate that the nonlinear effect transfers the energy from average flow and primary modes to high order modes, and all harmonic modes get to certain high energy levels, PSE method can well capture the two-and three-dimensional large scale vortex structures in supersonic mixing layers.