The Couette-Poiseuille Inhomogeneous Shear Flow at the Motion of the Lower Boundary of the Horizontal Layer

Goruleva, L. S.; Prosviryakov, Evgenii

doi:10.15350/17270529.2021.4.36

Cited by 4 publications

(2 citation statements)

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“…In this case the increase in fluid velocities can occur and there exist reverse flows. In [58][59][60], the influence of pressure gradients on the inhomogeneous flows of a vertical vortex flow was studied.…”

Section: Introductionmentioning

confidence: 99%

“…In [54][55][56][57][58][59][60], use was made of an inhomogeneous velocity field which satisfies exactly the Navier -Stokes equations, to solve the problem of convection of a vertical vortex flow. Using an exact solution for the velocity field [54][55][56][57][58][59][60], an inhomogeneous Couette flow was considered in [61] in specifying the temperature gradients on the upper boundary. It was shown that the motion of the boundary leads to intensification of heat conduction from the heated boundary.…”

Section: Introductionmentioning

confidence: 99%

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An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Berestova¹,

Prosviryakov²

2023

Nelin. Dinam.

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An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

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Section: Introductionmentioning

confidence: 99%