On the origin of spanwise vortex deformations during the secondary instability stage in compressible mixing layers

The three-dimensionality of turbulence initiates with spanwise vortex deformations associated with the amplification of three-dimensional disturbance modes. However, the origin of spanwise vortex deformations is still not well understood. In this paper, compressible mixing layers are performed via direct numerical simulation (DNS). Two typical types of secondary instabilities producing spanwise vortex deformations are of consideration: fundamental instability and subharmonic instability. Based on the fast Fourier transform and DNS data, a low-rank velocity model v(0) is obtained to demonstrate that spanwise vortex deformations are originated from a linear superposition of fundamental norm mode, a pair of fundamental or subharmonic oblique modes, and the mean mode. Through observing flow structures of the above norm and oblique modes, a striking feature is found that the velocity model v(0) containing deformed spanwise vortices can be decomposed into three new velocity models v(1), v(2), and v(3) containing relatively simplified counterparts (spanwise or oblique vortices). Then, the instability mechanism of the latter vortices is explored by analyzing the position relationship between the function of the generalized inflection points and cores of relatively simplified vortices. We find that an inviscid inflectional instability mechanism is responsible for the formation of spanwise and oblique vortices. Based on the above findings, a view is first proposed that spanwise vortex deformations with aligned and staggered patterns are a joint result of the parametric resonant mechanism and the inviscid inflectional instability mechanism.