Sensitivity analysis of a streamwise corner flow

Abstract

The stability of the flow formed by the intersection of two perpendicular flat plates is revisited through a study of the sensitivity to base-flow variations. After a brief presentation of the asymptotic regime, sensitivity functions underlying corner mode (concentrated close to the intersection) and Tollmien–Schlichting modes, with different obliqueness angles, are computed. Taking this into consideration, associated mechanisms as well as active regions are identified, which further confirm the sensitivity area of the corner mode along the intersection of two flat plates. Furthermore, the concept of ΔU-pseudospectra indicates that under a small base-flow modification, a certain range of frequencies underlying the corner mode could become unstable. Then, an optimization technique tracking the worst-case scenario, i.e., the deviation leading to a maximum temporal amplification rate, shows that a small variation in the reference field in the area of uncertainty leads to a significant decrease in the critical Reynolds number as observed in experiments. A hypothesis based on the onset of an inflectional mechanism is thus proposed to explain the experimental results.