An exact solution for the description of the gradient flow of a vortex fluid

Abstract

An isothermal nonlinear gradient flow of a horizontal layer of a vertically vortex fluid is considered. The Navier-Stokes equation uses a solution describing the velocity and pressure fields. This solution is a linear function of the longitudinal (horizontal) coordinates with coefficients depending on the transverse (vertical) coordinate. For the obtained general exact solution, the boundary-value problem is solved with the no-slip conditions, nonzero tangential stresses, and constant pressure gradients set at the boundaries of the infinite fluid layer. It is shown that, for the considered boundary conditions, up to three stagnation points can arise in the fluid layer. The velocity or its components change their direction to the opposite at these stagnation points. © 2019 Author(s).