A Class of Exact Solutions of Two-Dimensional Viscous Flow

Abstract

A viscous two-dimensional flow of shear layers superimposed on a stagnation point flow is investigated. This situation allows an exact solution of unsteady Navier-Stokes equation of an incompressible fluid in free space for a general initial condition. The solution is exemplified for several sorts of initial condition. One of them represents a flow in a balance between viscous diffusion and convective confinement of vorticity in the final asymptotic state. Another shows a flow field of collision of two shear layers of opposite senses, which is forced to come into contact by the imposed flow, and this collision results in ‘pair annihilation’ of the vortical layers. The decay of the vortex strength of the layer shows a similarlity behaviour for different Reynolds numbers. A comment is given about a possible dissipation mechanism in free flows.