Analysis of non-one-dimensional shear concentration convective flows of a viscous incompressible fluid in a plane horizontal layer with motionless boundaries

Abstract

Increased mineralization of some fluid layers in companson with that of the other layers causes the appearance of concentration-induced convection. This type of convection is most pronounced for brines of surface water bodies, salt marshes, saline rocks, etc. Nevertheless, concentration-induced convection occurs not only in natural reservoirs, but also in technical devices due to the inhomogeneous distribution of vanous impurities in hydraulic media. The characteristics of impurity distribution have a significant effect on the flow charactenstics. The paper considers a shear convective flow of a viscous incompressible fluid in a horizontal layer, which is induced by the nonuniform distribution of impurity concentration. A system of equations for concentration-induced convection is used to descnbe such flows; a solution is sought among classes of generalized solutions. As the boundary conditions, it is assumed that the no-slip condition is satisfied at the lower impermeable boundary, that the upper boundary of the layer is motionless, and that the distribution of salinity and pressure is specified on it. A solution to the descnbed boundary value problem is obtained. The attention is focused on the analysis of the properties of the flow velocity field. The conditions at which the flow reduces to a unidirectional one are denved. It is shown that none of the velocity field components can vanish inside the fluid layer, i.e. that the fluid layer cannot be divided into zones in such a way that the fluid would change the flow direction when transiting from one zone to another. © 2020 American Institute of Physics Inc.. All rights reserved.