A PAIR OF STREAM FUNCTIONS FOR 3-DIMENSIONAL VORTEX FLOWS

Introducing a vector potential, that is based on a pair of stream func tions, and a velocity potential, antisymmetric equations for the strea m functions are derived with the help of a variational principle. It i s found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymme tric flows with downstream helical flows. The special case of a transi tion from an upstream solid-body vortex to a downstream helical flow i s investigated in detail. Furthermore, the stream-function equations a re particularly useful to investigate general small- amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-ind ependent in a suitably rotating frame of reference can also be discuss ed with the proposed method.