The problem of a viscous vortex core embedded in an unsteady outer potential swirling flow is considered. By introducing a suitable similarity variable, the full Navier–Stokes equations for the unsteady axisymmetric flow of an incompressible fluid are reduced to two ordinary differential equations. These are solved numerically. When the radial flux of a particular outer potential flow satisfies certain conditions a family of three-cell core structures is possible. This family is not represented by any known analytical solution.
This work is useful for studying meteorological flow systems such as tornadoes. In particular, it suggests how two- and three-cell structures can develop from a one-cell structure and also shows the sensitivity of the core flow to small changes in the outer potential flow.