Layered Three-Dimensional Nonuniform Viscous Incompressible Flows

Abstract

An exact solution of Navier–Stokes equations for laminar flows of a viscous incompressible liquid under constant pressure is presented. The solution describes the balance of nonlinear viscous forces and inert effects in a liquid. It shows that the exact solution is a linear superposition of the shear flow and vertical rotation of the liquid caused by the nonuniform boundary conditions on a free boundary. Accounting for the inertia forces allows studying the delamination of the velocity field (counterflows) by the vertical coordinate depending on the horizontal velocities and spatial acceleration. The corresponding sets of algebraic inequalities are presented.