DNS Investigation of the Breakdown Mechanics of Görtler Vortices in Hypersonic Flows

In this paper we investigate the transition in hypersonic boundary layers over concave surfaces using direct numerical simulation (DNS). Our focus is on the breakdown of Görtler vortices and the transition to fully turbulent boundary layer, assuming a hypersonic flow at moderate Mach number that allows us to consider the calorically perfect gas condition. More specifically, a Mach $6$ or $7$ boundary layer flow over an adiabatic or isothermal concave wall is disturbed in the upstream to excite centrifugal instabilities in the form of Görtler vortices. Downstream, high- and low-speed streaks develop in the flow, eventually evolving into mushroom-like structures before breaking into turbulence. The parametric study includes the variation of the spanwise separation of these vortices while keeping the boundary layer thickness constant at a Reynolds number based on the momentum thickness of $1,500$ and the corresponding Görtler number of $11$. Among various flow characteristics results, consisting of iso-surfaces of Q-criterion, contour plots, energy and wall shear stress distributions, as well as periodicity analysis, we also include spectral proper decomposition (SPOD) analysis, which is a frequency-domain extension of POD, which identifies coherent structures that oscillate at specific frequencies. From our numerical simulation results, we observe that for large spanwise separation the periodicity of Görtler vortices is maintained for longer distances in the turbulent boundary layer compared to smaller spanwise separation, and that the breakdown process is dominated by a sinuous-type instabilities for adiabatic walls, and a combination of varicose- and sinuous-type for isothermal walls.