# Transient growth analysis of oblique shock wave/boundary-layer interactions at Mach 5.92

## TL;DR

This study investigates how transient growth mechanisms in high-speed boundary layers interacting with oblique shock waves can lead to flow perturbation amplification, highlighting non-modal effects relevant for hypersonic flow transition.

## Contribution

It introduces a power-iteration approach to quantify transient growth in compressible boundary layers with shock interactions, revealing the significant impact of shock waves on flow perturbation amplification.

## Key findings

- Oblique waves dominate transient response without shock.
- Oblique shock waves increase transient growth significantly.
- Base flow deceleration near reattachment amplifies streaks.

## Abstract

We study physical mechanisms that trigger transient growth in a high-speed spatially-developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power-iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstrate that the presence of the oblique shock wave significantly increases transient growth over short time intervals through a mechanism that is not related to a slowly growing global instability. The resulting response takes the form of spanwise periodic streamwise elongated streaks and our analysis of the linearized inviscid transport equations shows that base flow deceleration near the reattachment location contributes to their amplification. The large transient growth of streamwise streaks demonstrates the importance of non-modal effects in the amplification of flow perturbations and identifies a route for the emergence of similar spatial structures in transitional hypersonic flows with shock wave/boundary-layers interaction.