A Class of Exact Solutions of Two-Dimensional Viscous Flow

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.