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This article is cited in 3 scientific papers (total in 3 papers)
Nonlinear physics and mechanics
Exact Solutions to the Navier – Stokes Equations
for Describing the Convective Flows
of Multilayer Fluids
N. V. Burmashevaab, E. Yu. Prosviryakovba a Ural Federal University,
ul. Mira 19, Ekaterinburg, 620002 Russia
b Instutute of Engineering Science, Ural Branch of the Russian Academy of Sciences,
ul. Komsomolskaya 34, Ekaterinburg, 620049 Russia
Abstract:
In this paper, we report on several classes of exact solutions for describing the convective
flows of multilayer fluids. We show that the class of exact Lin – Sidorov – Aristov solutions is
an exact solution to the Oberbeck – Boussinesq system for a fluid discretely stratified in density
and viscosity. This class of exact solutions is characterized by the linear dependence of the
velocity field on part of coordinates. In this case, the pressure field and the temperature field
are quadratic forms. The application of the velocity field with nonlinear dependence on two
coordinates has stimulated further development of the Lin – Sidorov – Aristov class. The values
of the degrees of the forms of hydrodynamical fields satisfying the Oberbeck – Boussinesq equation
are determined. Special attention is given to convective shear flows since the reduced Oberbeck –
Boussinesq system will be overdetermined. Conditions for solvability within the framework of
these classes are formulated.
Keywords:
exact solution, multilayer fluids, Oberbeck – Boussinesq equations, shear flows,
self-similar flows with spatial acceleration.
Received: 06.07.2022 Accepted: 16.08.2022
Citation:
N. V. Burmasheva, E. Yu. Prosviryakov, “Exact Solutions to the Navier – Stokes Equations
for Describing the Convective Flows
of Multilayer Fluids”, Rus. J. Nonlin. Dyn., 18:3 (2022), 397–410
Linking options:
https://www.mathnet.ru/eng/nd801 https://www.mathnet.ru/eng/nd/v18/i3/p397
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Abstract page: | 128 | Full-text PDF : | 62 | References: | 32 |
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