Comprehensive experimental and computational investigations have revealed possible mechanisms underlying low-frequency unsteadiness observed in spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLI). In the present work, we extend this understanding by examining the dynamic linear response of a moderately separated Mach 2.3 STBLI to small perturbations. The statistically stationary linear response is analysed to identify potential time-local and time-mean linear tendencies present in the unsteady base flow: these provide insight into the selective amplification properties of the flow at various points in the limit cycle, as well as asymmetry and restoring mechanisms in the dynamics of the separation bubble. The numerical technique uses the synchronized large-eddy simulation method, previously developed for free shear flows, significantly extended to include a linear constraint necessary for wall-bounded flows. The results demonstrate that the STBLI fosters a global absolute linear instability corresponding to a time-mean linear tendency for upstream shock motion. The absolute instability is maintained through constructive feedback of perturbations through the recirculation: it is self-sustaining and insensitive to external forcing. The dynamics are characterized for key frequency bands corresponding to high–mid-frequency Kelvin–Helmholtz shedding along the separated shear layer $(St_{L}\sim 0.5)$, low–mid-frequency oscillations of the separation bubble $(St_{L}\sim 0.1)$ and low-frequency large-scale bubble breathing and shock motion $(St_{L}\sim 0.03)$, where the Strouhal number is based on the nominal length of the separation bubble, $L$: $St_{L}=fL/U_{\infty }$. A band-pass filtering decomposition isolates the dynamic flow features and linear responses associated with these mechanisms. For example, in the low-frequency band, extreme shock displacements are shown to correlate with time-local linear tendencies toward more moderate displacements, indicating a restoring mechanism in the linear dynamics. However, a disparity between the linearly stable shock position and the mean shock position leads to an observed asymmetry in the low-frequency shock motion cycle, in which upstream motion occurs more rapidly than downstream motion. This is explained through competing linear and nonlinear (mass depletion through shedding) mechanisms and discussed in the context of an oscillator model. The analysis successfully illustrates how time-local linear dynamics sustain several key unsteady broadband flow features in a causal manner.

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The separation length employed to scale unsteady phenomena in strong (separated) nominally two-dimensional (2-D) shock/turbulent-boundary-layer interactions cannot be directly extended to three-dimensional (3-D) swept interactions, due to the quasi-conical symmetry of 3-D interactions. This paper examines the issue by considering large-eddy simulations of Mach 2 canonical flows arising from plate-mounted swept compression ramps and sharp fins at various interaction strengths, which have been the subject of concurrent experimental campaigns. Several key structural features are discussed that distinguish 3-D interactions from 2-D interactions in the context of free-interaction principles and quasi-conical symmetry, including their relationship to strong crossflow and open separation. The virtual-conical-origin concept is augmented by considering inceptive effects, which motivate the introduction of an inceptive origin. The dependence of the inceptive-origin/virtual-conical-origin relationship with interaction strength yields several insights and provides a more rigorous framework to quantify inception strength than previously available. Finally, examination of the spanwise dependence of the growth of the quasi-conical separated shear layer shows that the outer (main) layer exhibits spanwise-homogeneous symmetry consistent with 2-D free-interaction theory, whereas the inner layer exhibits conical symmetry, consistent with 3-D (conical) free-interaction theory. The ramifications for shear layer and shock unsteadiness, as well as acceleration of the inner layer and secondary separation, are discussed. Recent developments and persisting fundamental challenges are discussed by Clemens and Narayanaswamy [2] and Gaitonde [3]. Significant insight has been gained through recent experimental and high-fidelity numerical efforts for canonical two-dimensional (2-D) configurations, which are spanwise homogeneous apart from side-wall effects. These include the impinging shock [4-7] and compression ramp [8,9] interactions. Comparatively less attention has been focused on the unsteady properties of canonical three-dimensional (3-D) STBLIs. These include configurations for which the mean flow is 3-D; that is, interactions that exhibit spanwise nonhomogeneity caused by the geometry/orientation of the shock generator which cannot be attributed to edge/side-wall effects. Specifically, interactions in which the shock or obstacle is swept with respect to the incoming flow are of interest. These include the sharp-fin (SF), swept-compression-ramp (SCR), and swept-impinging-shock (SIS) configurations, as commonly described [3,10]. Such interactions are of particular concern in application to supersonic/hypersonic inlets with side-wall compression, because side-wall compression may be exploited to increase the total pressure recovery [11,12]. More complex scenarios include flows with multiple interactions (shock trains) in scramjet inlet/ isolator sections, which highlight complexities associated with the dynamic coupling between canonical i...

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