Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid
AU - Berestova, S. A.
AU - Prosviryakov, E. Yu.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85152799184
UR - https://elibrary.ru/item.asp?id=54237550
U2 - 10.20537/nd230201
DO - 10.20537/nd230201
M3 - Article
VL - 19
SP - 167
EP - 186
JO - Russian Journal of Nonlinear Dynamics
JF - Russian Journal of Nonlinear Dynamics
SN - 2658-5324
IS - 2
ER -
ID: 37492236