Asymptotic Multiscale Solutions to Navier–Stokes Equations with Fast Oscillating Perturbations in Boundary Layers
Vladimir G. Danilov, R. K. Gaydukov · Russian Journal of Mathematical Physics · 2022
Abstract A problem of a nonstationary incompressible viscous fluid flow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or the triple-deck structure boundary layers on the plate. In the paper, we present a rigorous approach to the solution construction. It appears that, despite the long-term history, the triple-deck theory should be revised and the well-known Benjamin–Ono equation does not appear in this theory.