Oblique transition in hypersonic double-wedge flow: An input-output viewpoint

The paper explicitly computes the input–output gain surface and reports two dominant peaks at (ω,λz) = (0, 1.5) and (0.4, 3) using resolvent SVD, with the steady peak dominant; these findings are documented in Figure 4 and the surrounding text, and are further corroborated by spatially localized analyses (Gxout) that highlight strong amplification of ω ≈ 0.4 oblique waves in the separation zone and steady streak amplification near reattachment . The paper also demonstrates via a weakly nonlinear expansion that quadratic interactions of oblique waves at ±ω, spanwise wavenumber β, generate steady streaks at 2β (hence spanwise wavelength halving), with the steady response obtained by applying the ω = 0 resolvent to the quadratic forcing; this is shown in equations (4.4)–(4.7) and Figure 9 (λstreakz = λobliquez/2) . Finally, the streamline-aligned energy budget shows that, for oblique waves, curvature Kc enters the transport of the shear stress Rsn and, together with base-flow deceleration ∂s ūs < 0, drives the growth of Es via the coupled system (3.11a)–(3.11b) and its reduction to (3.12); concave curvature Kc < 0 in the separated shear layer destabilizes the system, while deceleration dominates the amplification of steady streaks near reattachment . By contrast, the model’s Part A invokes an eigenvalue–resolvent pole argument that assumes local spectral structure and non-normality bounds without verification for the specific operator; it is thus assumption-laden and not established by the paper. More importantly, in Part C the model inserts an explicit curvature term −2 Kc ūs Rsn in the Es-equation and claims curvature-assisted growth when Kc > 0, which contradicts the paper’s formulation where curvature primarily enters the Rsn equation, and concave curvature Kc < 0 in the separated layer is shown to be destabilizing and to foster Es growth via coupling, not through a direct term in Es; near reattachment, the paper’s analysis shows deceleration dominates, consistent with the paper but at odds with the model’s sign conditions for curvature .