Features of selecting boundary conditions when describing flows of stratified fluids

Abstract

The article discusses the selection of boundary conditions at the boundary between adjacent layers in a stratified viscous incompressible fluid. It is shown that the "continuity condition + differentiability condition" pair traditionally used in many disciplines gives physically unjustified properties of the resulting exact solution for the velocity field. Although the condition for the differentiability of velocities is close in mathematical form to the stress continuity condition (by virtue of Newton’s law), in terms of physics, taking these conditions into account gives fundamentally different properties of the exact solution of the Navier-Stokes system of equations. It is shown that the consideration of the "the velocity field continuity condition + the stress field continuity condition" pair is more adequate to the physics of the process, which is consistent with the hypothesis of continuity.