The viscous tornado

A separation point can be thought of as a critical point, i.e. a point where instantaneous streamline solutions have indeterminate slopes. A whole variety of complex three-dimensional flow patterns near a separation point at a boundary have been classified. The present investigation is concerned with a critical point, taking into account an extension to unsteady flow. A critical point is a point of zero vorticity and in unsteady flow, this point can actually translate along the boundary generating, as it moves, an extremely complex network of streaklines which bear a resemblence to dye traces seen in turbulent boundary layers. The solutions obtained are asymptotically exact and to the linearized approximation only viscous forces and pressure gradient forces are involved. Some experimental observations are also presented. It is found that complex eigenvalue critical points or 'viscous tornadoes' occur in a variety of flow situations.