The steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady two-cell viscous vortex solutions which behave asymptotically as certain analogous unsteady one-cell solutions of Rott (1958). The radial flux is a parameter of the solution, and the effect of the radial flow on the circumferential velocity, is analyzed. The work suggests an explanation for the eventual dissipation of meteorological flow systems such as tornadoes.

A given axisymmetric potential swirling flow is bounded by a plane perpendicular to the axis of symmetry. By the no slip condition, viscous effects will be important over the plane and since the circumferential velocity must be zero on the axis of symmetry, viscous effects will also be important in the core of the vortex. These two viscous regions will overlap near the intersection of the axis of symmetry with the plane. Thus the flow field can be divided into four regimes, the viscous core, the boundary layer on the plane, a 'stagnation point' regime and the given potential flow which provides the outer boundary conditions for each of the first two regimes. Such a model could be useful for studying meteorological flow systems such as tornadoes. The viscous core regime has already been studied (Rott, 1958(Rott, , 1959Bellamy-Knights, 1970, 1971).

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