Analytical study of the Ekman angle for the Benard–Marangoni convective flow of viscous incompressible fluid

Abstract

The paper considers the convective flow of a viscous incompressible fluid over a rotating surface. It studies the angle between the fluid velocity vector in the upper layer and the temperature gradient vector on the free surface. For the study, an analytical solution to the Oberbeck–Boussinesq equations is constructed, which describes the stratified Ekman flow taking into account two components of the Coriolis force. The temperature gradient and the conditions of Marangoni thermocapillary convection are set at the upper (free) boundary, and the condition of fluid adhesion is set on the lower (solid) boundary. The representation of velocities in the form of linear functions of horizontal coordinates is used. It is shown that, when the flow depth tends to infinity, the angle between the upper layer fluid velocity vector and the temperature gradient vector tends to π/2 .