Numerical study of the exact solution of the Navier–Stokes equation describing free-boundary fluid flow

This paper presents a numerical study of the partially invariant solutions of the Navier–Stokes equations for the plane case which describes unsteady flow in a layer bounded by a straight solid wall and a free boundary parallel to it. It is found that for different values of the initial flow velocity, there may be the establishment a steady state with a decrease or an increase in the initial layer thickness can be established or the layer thickness can be increased infinitely due to liquid inflow from infinity.