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Approximations of the Navier–Stokes equations for high Reynolds number flows past a solid wall. (English) Zbl 1107.76024

Summary: Approximations of the Navier–Stokes equations at high Reynolds number near solid boundaries are studied by using a method of successive complementary expansions. The starting point of the method is to look for a uniformly valid nonregular approximation. No matching principle is required to construct the approximation. The application of this method leads rigorously to the theory of interactive boundary layer which relies upon generalized boundary layer equations strongly coupled to the inviscid equations for the outer stream.
It is shown that the interactive boundary layer model contains the Prandtl boundary layer model and the triple deck model. These two models are two different regular expansions of the interactive boundary layer which are deduced asymptotically, i.e., when the Reynolds number goes to infinity.
Applications of the interactive boundary layer model to boundary layers influenced by external vorticity are presented and compared with Navier–Stokes solutions.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
34E05 Asymptotic expansions of solutions to ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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