Fig. 1. (a) Schematic of aero-optic effects of an infrared guidance vehicle; (b) wavefront distortion caused by a vortex.

Fig. 2. The vorticity contour of a supersonic mixing layer simulated by LES.

Fig. 3. Process of establishing an elliptic model for the vortex boundary: (a) Two vortices; (b) LCS; (c) elliptic model of vortex boundary

Fig. 4. Schematic of calculating position coordinates of a vortex core.

Fig. 5. Method of representing fluid density distribution inside a vortex based on its boundary and core location.

Fig. 6. (a)The supersonic mixing layer with Mc = 0.5; (b) Vortex A; (c) Vortex B; (d) Vortex C.

Fig. 7. Density distribution of fluid inside three vortices: (a) Density distribution of fluid inside Vortex A along the flow direction (x-axis); (b) density distribution of fluid inside Vortex A along the longitudinal direction (y-axis); (c) density distribution of fluid inside Vortex B along the flow direction (x-axis); (d) density distribution of fluid inside Vortex B along the longitudinal direction (y-axis); (e) density distribution of fluid inside Vortex C along the flow direction (x-axis); (f) density distribution of fluid inside Vortex C along the longitudinal direction (y-axis).

Fig. 8. Supersonic mixing layers with different compressibilities

Fig. 9. Density distribution of fluid inside two vortices in the supersonic mixing layers with different compressibilities.

Fig. 10. (a) Supersonic mixing layer with Mc = 0.3; (b) two adjacent vortices during their merging process.

Fig. 11. Variation curve of the fluid density inside the vortex a and b during their merging process.

Fig. 12. Variation of fluid density at several characteristic points during their merging process.

Fig. 13. (a) The supersonic mixing layer with different inflow density of its upper and lower layers; (b) density distribution of fluid inside the vortex along the longitudinal direction (y-axis); (c) density distribution of fluid inside the vortex along the flow direction (x-axis).