An inhomogeneous Couette-type flow with a perfect slip condition at the lower boundary of an infinite fluid layer

Abstract

In this paper, we investigate an exact solution to the three-dimensional problem of an isobaric flow of a viscous incompressible fluid layer. The solution is a linear function of the longitudinal coordinates. The solution type under study describes a vertical twist in the fluid, which arises due to the inclusion of inertial forces and inhomogeneous velocity distribution at the free boundary of the fluid layer. The solution allows to us describe the counterflow of an incompressible fluid in a thin layer. The exact solution is obtained for the perfect slip condition at one of the boundaries of the fluid layer. Conditions for the existence of points inside the fluid layer at which the velocity vanishes are defined. © 2019 Author(s).