Current Research:

Hollow Vortices

Hollow vortices are characterized by a slowly rotating center (weak vorticity), surrounded by a high speed circumferential jet (strong vorticity). They occur in geophysical flows and include the Antarctic Stratospheric vortex corresponding to the ozone hole and the Great Red Spot (GRS) on Jupiter. Other examples occur in plasmas.

Most numerical simulations show that a vortex which is too hollow (i.e., vorticity too weak at the center) is violently unstable. The vortex breaks apart and reassembles so that the strongest vorticity is at the center and the weakest is at the outer edge. These dynamics occur on the order of a few turn-around times of the vortex. This poses the question of how stable hollow vortices such as the GRS can exist in nature, contrary to numerical simulations.

Our research indicates that a hollow vortex can be stabilized by placing it near a strong gradient in potential vorticity. It is also plausible that a hollow vortex can sustain itself against dissipation in a statistically steady equilibrium by accreting small, intense vortices at its edges, while the vortex center decays. This creates a hollowness that increases over time. When the hollowness reaches a certain critical value, an instability occurs and vorticity avalanches toward the center of the vortex bringing the hollowness below the critical limit. This is perhaps analogous to sand avalanching down a sand pile which has reached its critical angle of repose.

Research Interests

Fluid Mechanics, Numerical Methods, Physically-Based Modeling in Computer Graphics, Computational Geometry, Bio-Mechanics