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The lift-off characteristics of supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI for short), extracted from a wall-mount ramp injector in scramjet, is studied through Large-eddy simulation method. Shocked helium jet is deformed into a pair of streamwise vortex with a co-rotating companion vortex showing the lift-off characteristic immediately after shock. Based on the objective coordinate system in frame of oblique shock structure, it is found that the nature of three-dimensional lift-off structure of a shockinduced streamwise vortex is inherently and precisely controlled by a two-stage growth mode of structure kinetics of a shock bubble interaction (SBI for short). The striking similar structures between OS/JI and SBI support the proposition that the lift-off of streamwise vortex is the result of a underlying two-dimensional vortical motion. By considering the first stage impulsive linear growth rate, an improved vortex propagation model suitable for SBI is proposed and validated. The lift-off phenomena of both numerical OS/JI case in this paper and wall-mounted ramp injector cases in literature are well explained under the two-stage structure kinetics model of SBI. This model further predicts that for higher free stream Mach number (M > 5), increasing ramp compression shows little effect on elevating streamwise vortex while evident lift-off may occur for lower Mach number (M < 3.5), which offers the new way for preliminary design of streamwise vortex-based ramp injector in scramjet.