Geodesic
Plane-Parallel Advective Flow in a Horizontal Layer of
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 2, pp. 219-226.

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In this paper a new exact solution of the Navier – Stokes equations in the Boussinesq approximation describing advective flow in a horizontal liquid layer with free boundaries, where the vertical velocity component is a constant value, is obtained. The temperature is linear along the boundaries of the layer. Solutions of this kind are used to close three-dimensional equations averaged across the layer in the derivation of two-dimensional models of nonisothermal large-scale flows in a thin layer of liquid or incompressible gas. The properties of advective flow at different values of Reynolds number and Prandtl number are investigated.
Keywords: advective flow, Navier – Stokes equation.
Mots-clés : exact solution 
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K. G. Shvarts. Plane-Parallel Advective Flow in a Horizontal Layer of. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/ND_2023_19_2_a3/

[1] Teoret. Osnovy Khim. Tekhnolog., 50:3 (2016), 294–301 (Russian \goodbreak) | DOI

[2] Burmasheva, N. V. and Prosviryakov, E. Yu., “A Class of Exact Solutions for Two-Dimensional Equations of Geophysical Hydrodynamics with Two Coriolis Parameters”, Izv. Irkutsk. Gos. Univ. Ser. Matem., 32 (2020), 33–48 (Russian) | MR | Zbl

[3] Burmasheva, N. V. and Prosviryakov, E. Yu., “Exact Solutions to the Navier – Stokes Equations Describing Stratified Fluid Flows”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 25:3 (2021), 491–507 | DOI | Zbl

[4] Burmasheva, N. V., Larina, E. A., and Prosviryakov, E. Yu., “A Couette-Type Flow with a Perfect Slip Condition on a Solid Surface”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2021, no. 74, 79–94 (Russian) | MR

[5] Gershuni, G. Z., Zhukhovitskii, E. M., and Nepomnyashchii, A. A., Stability of Convective Flows, Nauka, Moscow, 1989, 320 pp. (Russian) | MR | Zbl

[6] Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana, 54:2 (2018), 213–220 (Russian) | DOI

[7] Ivantsov, A. O., “Weakly Non-Linear Analysis of Thermoacoustic Advective Flow”, Vestn. Permsk. Gos. Univ. Fizika, 2019, no. 3, 28–44 (Russian)

[8] Mizev, A., Mosheva, E., Kostarev, K., Demin, V., and Popov, E., “Stability of Solutal Advective Flow in a Horizontal Shallow Layer”, Phys. Rev. Fluids, 2:10 (2017), 103903, 16 pp. | DOI

[9] Harun, M. H., Didane, D. H., Sayed Abdelaal, M. A., Zaman, I., and Manshoor, B., “Exact Solutions to the Navier – Stokes Equations for Nonlinear Viscous Flows by Undetermined Coefficient Approach”, J. Complex Flow, 3:2 (2021), 38–41

[10] Prikl. Mekh. Tekhn. Fiz., 58:2 (2017), 90–97 (Russian) | DOI | MR

[11] Prikl. Mekh. Tekhn. Fiz., 58:4 (2017), 135–141 (Russian) | DOI | MR

[12] Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 2020, no. 1, 33–44 (Russian) | DOI | MR | MR | Zbl

[13] Prikl. Mat. Mekh., 82:1 (2018), 25–30 (Russian) | DOI | MR | Zbl

[14] Shvarts, K. G. and Shklyaev, V. A., Mathematical Modeling of Mesoscale and Large-Scale Process of Transfer of Impurities in a Baroclinic Atmosphere, IKI, Izhevsk, 2015, 156 pp. (Russian)