Görtler instability and transition in compressible flows

We present a discussion on theoretical, experimental, and computational research studies on Görtler instability and the related transition to turbulence occurring in compressible boundary layers over concave surfaces. We first examine the theoretical results on primary and secondary instabilities, emphasizing the role of receptivity, the mechanism by which external agents, such as freestream fluctuations or wall roughness, act on a boundary layer to trigger Görtler vortices. We review experimental findings obtained from measurements in supersonic and hypersonic wind tunnels and discuss studies employing numerical methods, focusing on the direct numerical simulation approach. The research in these two last sections is surveyed according to the geometrical configuration, from simple concave walls to more complex surfaces of hypersonic vehicles. The experimental investigations have been successful in the visualizations of Görtler vortices, in the measurement of the wall-heat transfer in the transitional region, and in the computation of the Görtler-vortex growth rates, although detailed boundary-layer velocity measurements are still missing. Direct numerical simulations have confirmed instability results emerging from stability theories and revealed nonlinear interactions between Görtler vortices and other disturbances. The established initial-boundary-value receptivity theory can certainly benefit from more advanced experimental measurements, and receptivity results should be used in combination with direct numerical simulations. A major conclusion of our review is therefore that the understanding of Görtler vortices should be pursued by a combined methodology including theoretical analysis based on the receptivity formalism, direct numerical simulation, and experiments. Highly desirable outcomes of such endeavor are the prediction of the location and extension of the transition region, and a model for the transition process. We finally highlight further prospects and challenges on fundamental and applied research on Görtler instability and transition in compressible flows.