Linear and nonlinear growth of secondary instabilities of crossflow vortices studied by PSE

Abstract

Laminar-turbulent transition in (quasi-) three-dimensional boundary layers dominated by crossflow vortices is studied for the setup of the DLR swept-flat plate experiment. The linear and subsequent nonlinear stages of both the crossflow vortices and their high-frequency secondary instabilities are modelled by nonlinear parabolized stability equations (PSE). In the first part of the talk it is shown that those high-frequency secondary instabilities may develop from the interaction of stationary and low-frequency travelling crossflow vortices, a transition scenario usually more relevant in wind-tunnel experiments. In low-turbulence-level environments like free flight with stationary crossflow vortices being dominant in amplitude the high-frequency secondary instabilities presumably are triggered directly from environmental disturbances via a receptivity mechanism, however. Therefore, in the second part results from a different approach developed recently based on a bi-directional coupling between a secondary instability code and a PSE code are presented. Thereby, the nonlinear development of secondary instabilities including the generation of higher harmonics could be studied up to the stages where the feedback of the finite-amplitude secondary instability modes on the stationary crossflow vortices is no longer negligible and the skin-friction coefficient starts to deviate from that due to the mean flow distortion caused by the stationary crossflow modes alone. The latter could be used as a criterion for imminent laminar-turbulent transition within the saturation region of the stationary crossflow modes which was lacking in a nonlinear PSE analysis of crossflow-dominated transition until now.