Axisymmetric Vortex Solution of Navier-Stokes Equation

抄録

An exact solution of a viscous incompressible flow is presented for a general initial condition. This flow represents an axisymmetric shear layer superimposed on an irrotational straining flow. The solution incorporates the three representative features of vortex motion: stretching, convection and viscous diffusion. In a particular case of constant straining, the flow approaches to a steady state in which the above three effects are in equilibrium. However if the initial state is composed of the same amount of opposite vorticities, the shear layer disappears exponentially in time. Spectral analysis of the solution shows the cascade of vorticity fluctuations to smaller scales.
The general solution includes the vortex solutions given by Oseen (1911) and by Burgers (1948), and partly overlaps the similarity solution found by Bellamy-Knights (1970).