TY - JOUR

T1 - Numerical Construction of a Set of Zero Velocities and Countercurrents for Steady Dynamic Equilibria

AU - Prosviryakov, E. Yu.

AU - Sokolov, A. S.

PY - 2022/12/1

Y1 - 2022/12/1

N2 - A steady shear convective flow of a fluid moving between two rotating infinite planes (disks) is investigated. The angular velocities of the boundaries of an infinite horizontal layer are described by various quantities. In other words, the differential rotation of a medium (dynamic equilibria), instead of the solid-body rotation of the fluid (the Ekman convective flow), is studied. The exact solution of the Oberbeck-Boussinesq equations is considered. The system of equations is overdetermined, since, to determine four unknown functions for the shear convective flow, it is necessary to integrate a nonlinear system of partial differential equations from five equations. The velocity field is determined by linear forms. The temperature field and the pressure field are described by quadratic forms. The forms depend on two coordinates (horizontal or longitudinal). The form factor is determined by the connection from the vertical (third, transverse) coordinate. The exact solution used makes it possible to meet the "extra" equation (the incompressibility equation) and construct a nonlinear system of ordinary differential equations. The equations are numerically integrated to determine the hydrodynamic fields. The structure of countercurrents arising at the steady convection of a fluid is investigated. Using numerical algorithms for the systems of ordinary equations, the regions of the existence of countercurrents are built depending on the fluid parameters and boundary conditions for an infinite horizontal layer.

AB - A steady shear convective flow of a fluid moving between two rotating infinite planes (disks) is investigated. The angular velocities of the boundaries of an infinite horizontal layer are described by various quantities. In other words, the differential rotation of a medium (dynamic equilibria), instead of the solid-body rotation of the fluid (the Ekman convective flow), is studied. The exact solution of the Oberbeck-Boussinesq equations is considered. The system of equations is overdetermined, since, to determine four unknown functions for the shear convective flow, it is necessary to integrate a nonlinear system of partial differential equations from five equations. The velocity field is determined by linear forms. The temperature field and the pressure field are described by quadratic forms. The forms depend on two coordinates (horizontal or longitudinal). The form factor is determined by the connection from the vertical (third, transverse) coordinate. The exact solution used makes it possible to meet the "extra" equation (the incompressibility equation) and construct a nonlinear system of ordinary differential equations. The equations are numerically integrated to determine the hydrodynamic fields. The structure of countercurrents arising at the steady convection of a fluid is investigated. Using numerical algorithms for the systems of ordinary equations, the regions of the existence of countercurrents are built depending on the fluid parameters and boundary conditions for an infinite horizontal layer.

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UR - https://elibrary.ru/item.asp?id=59259776

U2 - 10.1134/S1063785022110050

DO - 10.1134/S1063785022110050

M3 - Article

VL - 48

SP - 322

EP - 328

JO - Technical Physics Letters

JF - Technical Physics Letters

SN - 1063-7850

IS - 12

ER -