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

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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.

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Notes

  1. The symbol \(\ldots\) denotes any other variables.

  2. It is called the displacement thickness in the triple-deck structure theory

  3. Under the assumption that the initial value is the unperturbed plane-parallel flow (9).

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Funding

The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University).

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. G. Danilov & R. K. Gaydukov

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  1. V. G. Danilov
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  2. R. K. Gaydukov
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Correspondence to R. K. Gaydukov.

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Danilov, V.G., Gaydukov, R.K. Asymptotic Multiscale Solutions to Navier–Stokes Equations with Fast Oscillating Perturbations in Boundary Layers. Russ. J. Math. Phys. 29, 431–455 (2022). https://doi.org/10.1134/S1061920822040045

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