On the low-frequency unsteadiness in shock wave–turbulent boundary layer interactions

Abstract

The shock wave–turbulent boundary layer interaction over a compression corner is studied using global stability analysis (GSA) and resolvent analysis based on a separation of scales between the low-frequency, large-scale motions and the turbulent fluctuations. The GSA identifies a leading stationary mode, which becomes globally unstable as the ramp angle is beyond a critical value. For globally stable flows, the resolvent analysis captures two-dimensional and three-dimensional local maxima in optimal gain, both of which are due to modal resonance between the forcing and the leading global mode. Notably, the frequency-premultiplied optimal gain associated with two-dimensional disturbances peaks at a low frequency. For different interaction strengths, the peak frequencies collapse onto a universal value of 0.015 when non-dimensionalized using the length of the separation region and the free-stream velocity. A numerical simulation perturbed with the corresponding optimal forcing reveals that the response is in the form of a back-and-forth shock motion.

A review of the research progress of boundary layer theory

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Investigation of the Inverse Magnus Effect on a Rotating Sphere in Hypersonic Rarefied Flow

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