Asymptotic Multiscale Solutions to Navier–Stokes Equations with Fast Oscillating Perturbations in Boundary Layers

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, th...

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Bibliographic Details
Published in:Russian journal of mathematical physics 2022-12, Vol.29 (4), p.431-455
Main Authors: Danilov, V. G., Gaydukov, R. K.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Boundary layers
Decks
Fluid dynamics
Fluid flow
Incompressible flow
Irregularities
Mathematical and Computational Physics
Navier-Stokes equations
Perturbation
Physics
Physics and Astronomy
Reynolds number
Theoretical
Triple-deck theory
Viscous fluids
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Summary: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.
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920822040045