Self-similarity in boundary layers
Boundary layers control the transport of momentum, heat, solutes and other quantities between walls and the bulk of a flow. The Prandtl-Blasius boundary layer was the first quantitative example of a flow
profile near a wall and could be derived by an asymptotic expansion of the Navier-Stokes equation. For higher flow speeds we have scaling arguments and models, but no derivation from the Navier-Stokes
equation. The analysis of exact coherent structures in plane Couette flow reveals ingredients of such a more rigorous description of boundary layers. I will describe how exact coherent structures can be scaled to obtain self-similar structures on ever smaller scales as the Reynolds number increases.
A quasilinear approximation allows to combine the structures self-consistently to form boundary layers. Going beyond the quasilinear approximation will then open up new approaches for controlling and manipulating boundary layers.
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