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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 12, Pages 2081–2093
DOI: https://doi.org/10.31857/S0044466923120074
(Mi zvmmf11672)
 

Mathematical physics

Singularity formation in an incompressible boundary layer on an upstream moving wall under given external pressure

S. I. Bezrodnykha, V. B. Zametaeva, T. Kh. Chzhunb

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia
Abstract: The two-dimensional laminar flow of a viscous incompressible fluid over a flat surface is considered at high Reynolds numbers. The influence exerted on the Blasius boundary layer by a body moving downstream with a low velocity relative to the plate is studied within the framework of asymptotic theory. The case in which a small external body modeled by a potential dipole moves downstream at a constant velocity is investigated. Formally, this classical problem is nonstationary, but, after passing to a coordinate system comoving with the dipole, it is described by stationary solutions of boundary layer equations on the wall moving upstream. The numerically found solutions of this problem involve closed and open separation zones in the flow field. Nonlinear regimes of the influence exerted by the dipole on the boundary layer with counterflows are calculated. It is found that, as the dipole intensity grows, the dipole-induced pressure acting on the boundary layer grows as well, which, after reaching a certain critical dipole intensity, gives rise to a singularity in the flow field. The asymptotics of the solution near the isolated singular point of the flow field is studied. It is found that, at this point, the vertical velocity grows to infinity, viscous stress vanishes, and no solution of the problem exists at higher dipole intensities.
Key words: laminar boundary layer, separation, asymptotic method.
Received: 17.03.2023
Revised: 28.04.2023
Accepted: 20.06.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 12, Pages 2359–2371
DOI: https://doi.org/10.1134/S0965542523120060
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: S. I. Bezrodnykh, V. B. Zametaev, T. Kh. Chzhun, “Singularity formation in an incompressible boundary layer on an upstream moving wall under given external pressure”, Zh. Vychisl. Mat. Mat. Fiz., 63:12 (2023), 2081–2093; Comput. Math. Math. Phys., 63:12 (2023), 2359–2371
Citation in format AMSBIB
\Bibitem{BezZamChz23}
\by S.~I.~Bezrodnykh, V.~B.~Zametaev, T.~Kh.~Chzhun
\paper Singularity formation in an incompressible boundary layer on an upstream moving wall under given external pressure
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 12
\pages 2081--2093
\mathnet{http://mi.mathnet.ru/zvmmf11672}
\crossref{https://doi.org/10.31857/S0044466923120074}
\elib{https://elibrary.ru/item.asp?id=54912962}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 12
\pages 2359--2371
\crossref{https://doi.org/10.1134/S0965542523120060}
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