The paper describes the direct numerical simulation (DNS) of a spatially developing compressible mixing layer with a convective Mach number of 0.8. The work mainly studies on the evolution process and formation mechanism of vortex structures during the late stage of transition process. In flow visualizations, multiple ring-like vortices and multiple necklace-like vortices appear during the late stage of the transition process. These multiple necklace-like vortices have never previously been reported in a compressible mixing layer. The formation mechanism is presented that the Kelvin–Helmholtz instability (K–H instability) of shear layers is the root cause of multiple ring-like vortices and multiple necklace-like vortices. DNS results indicate that new shear layer regions form around the corresponding Λ-vortices as the result of the first ejection and sweep events from each Λ-vortex. As a consequence, ring structures form one by one because of the K–H instability of shear layers, which represents the formation of multiple ring-like vortices. As the flow proceeds, several new local shear layer regions are generated around the ring structures, induced by the second ejection and sweep events from the rings of the multiple ring-like vortices. Bridge structures are then induced one by one by the K–H instability of shear layers, representing the formation of multiple necklace-like vortices. In addition, DNS results show that, from the first multiple necklace-like vortex onward, dominant vortex structures develop separately in the upper and lower layers until flow runs into the fully developed turbulent state. In the process, vortex structures in the upper layer clearly lag behind those in the lower layer.

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The three-dimensionality of turbulence initiates with spanwise vortex deformations associated with amplification of three-dimensional disturbance modes. But 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 (FFT) and DNS data, a low-rank velocity model v0 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 v0 containing deformed spanwise vortices can be decomposed into three new velocity models v1, v2 and v3 containing relatively simplified counterparts (spanwise or oblique vortices). Then, the instability mechanism of the latter vortices is explored by analyzing the position relationship between 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.