Abstract
Unsteady problem of a viscous incompressible flow in free space is investigated, and a class of exact solutions of the Navier-Stokes equation is given for a general initial condition. This flow field represents several shear layers superimposed on an irrotational, three-dimensional straining flow. This solution incorporates the three representative aspects of vortex motion : stretching, convection and viscous diffusion of vorticity. The solution is exemplified for several kinds of initial condition. One of them represents a flow approaching a steady state in which the above three effects are brought to an equilbrium. Another solutions show collision of two shear layers in various arrangments : e. g. two parallel layers merge into a single layer, two antiparallel layers (in which the vortices in the two layers are in the opposite directions), disappear as pair annihilation and two layers merge like vectors by oblique collision. It is also shown that N shear layers, in general, merge like vectors.
