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D. Kuzdas, S. Braun:
"Regularization of the ill-posed spike formation stage in marginally separated boundary layer flows";
Talk: 91st GAMM Annual Meeting in Kassel, Kassel; 03-15-2021 - 03-19-2021.

Transition from laminar to turbulent flow can follow many different routes and is not yet fully understood. In this work we apply the method of matched asymptotic expansions to so-called `by‐pass´ transition which typically may be observed in the flow past the suction side of slender airfoils at small angles of attack or channel flows with suction. Here, the onset of turbulence is triggered by the repeated bursting of a laminar separation bubble if e.g. the angle of attack is raised above a certain critical value.

For asymptotically large Reynolds numbers the bursting of a laminar separation bubble can be described by various consecutive stages formulated as singular perturbation problems.

The starting point is a laminar wall‐bounded shear layer on the verge of separation for which classical boundary layer theory ceases to provide a valid description. The formation of closed reverse flow regions in the ensuing stage can be described with the viscous‐inviscid interaction theory of marginal separation. However, the appearance of finite time singularities in the solution and the associated breakdown of the model equations initiate the consecutive spike formation stage. In this interactive triple deck stage near wall fluid (vorticity) is ejected from the rear of the separation bubble, as is known from experimental observations.

A numerical scheme to solve the fully nonlinear unsteady triple deck interaction of the spike formation stage is presented. The unbounded physical domain of the asymptotic description is mapped onto a bounded computational domain and discretized using a Chebyshev spectral collocation method.

Since the Cauchy problem associated with the original triple deck formulation is ill-posed and prone to short scale instabilities, a regularization based on a composite asymptotic model comprising higher order effects (e.g. streamline curvature) has been developed. The impact of the regularization is discussed on the basis of the amplitude spectrum of relevant quantities.

Project Head Stefan Braun:
Bypass transition: an asymptotic approach