Vortex Dynamics.

A theoretical description of vortex breakdown incorporating the essential physical processes governing the occurrence, location, and strength of the phenomenon and suitable for design and control purposes, is under development. The strongly decelerated motions, which can have flow reversals and therefore provide a model for vortex breakdown events, found earlier in the course of this project for vortices of aerodynamic type, have been shown to be unstable to three-dimensional perturbations when the deceleration exceeds a threshold value. The nature of the instability agrees with experimental observations and supports a comprehensive theoretical framework for vortex breakdown previously outlined. New numerical algorithms useful for very large stability problems have been developed under grant sponsorship, and have been published or will be shortly submitted for publication. Several other stability and bifurcation problems for rotating pipe flows have been solved. Rotating pipe flows are the simplest known exact viscous flows bearing a qualitative resemblance to vortices with axial streaming, and serve as a convenient theoretical testbed on which to develop an understanding of vortex instability and subsequent nonlinear evolution.