The statistical characteristics of the translation and rotation motion of a separation shock in a hypersonic compression ramp flow are studied based on a time-resolved Schlieren image dataset. Both spectral analysis and Proper Orthogonal Decomposition (POD) indicate that the unsteady shock motion can be decoupled as low-frequency shock translation mode and high-frequency shock rotation mode. A statistical dual-Gaussian model is then proposed, in which the shock motion is described as a linear combination of two independent Gaussian processes corresponding to shock translation and shock rotation. Through a POD-mode-exclusion evaluation, it is found that this model can generally predict the statistics of full-order shock motion except for the asymmetry nature of the forth-and-back translation of the separation shock. Meanwhile, the statistics of reduced-order shock motion corresponding to pure shock rotation can be accurately predicted by the dual-Gaussian model. Additionally, a transitional shock motion characterized by strong intermittency is identified during the transition from biased shock translation to normal shock rotation.
Zhang et al. (Sun,) studied this question.