Coexistence of stationary Görtler and crossflow instabilities in boundary layers

Abstract

The coexistence of stationary Görtler and crossflow instabilities in boundary layers covering incompressible to hypersonic regimes is investigated by varying the local sweep angle, pressure gradient, wall curvature, and wall temperature using linear stability analysis. The results show that increasing the local sweep angle under a fixed concave curvature in incompressible boundary layers leads to the appearance of two unstable modes at certain sweep angles, which is conventionally known as the “changeover” regime between the crossflow and Görtler modes. This study identifies a synchronization between the two modes under this condition, which is similar to multiple Görtler modes and thus referred to as Görtler–crossflow modes. Three scenarios are presented to describe the possible development of these modal instabilities. In addition, increasing the concave curvature destabilizes the instability, while introducing a pressure gradient stabilizes the instability and results in a shrinkage of the unstable band of the spanwise wavenumber, as reported in the literature. In supersonic and hypersonic boundary layers, synchronization can occur near specific sweep angles and under cold wall conditions in supersonic boundary layers. As Mach number increases, the synchronization regime shifts toward lower sweep angles and wall temperature, in which the former reflects a decline in crossflow strength relative to Görtler instability, while the latter indicates the influence of thermal effects on synchronization. In hypersonic boundary layers, the crossflow instability is insignificant compared with the Görtler instability. No synchronization is identified under various parameter changes, and the first Görtler–crossflow mode dominates across the entire spanwise wavenumber ranges.