Prof. Jeffry Weiss, Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder

"Point Vortices in 3D Geophysical Fluids"

Abstract: Due to the combined effects of rapid planetary rotation, quantified by a small Rossby number, and stable stratification, geophysical fluids often self-organize into a vortex gas, a collection of well-separated longlived coherent vortices. It is useful to model these vortices as idealized structures with limited internal degrees of freedom. The simplest such model is point vortices, where the vorticity is concentrated at isolated points in space. Asymptotic expansion of the governing fluid equations for small Rossby number leads to, at first order, quasi-geostrophic (QG) dynamics, and, at next order, balanced dynamics. QG point vortices have been known since the 1980s. QG dynamics has the restriction that, while the flow fills 3D space, the velocity is purely horizontal. Large scale flows in atmospheres and oceans have small but important vertical velocities. The zero vertical velocity of QG makes it unable to capture many important geophysical phenomena. Balanced dynamics, however, does contain small nonzero vertical velocity and is thus useful in situations where the small vertical velocity is important. Here we present the first point vortex solution of 3D balanced dynamics. Analysis and simulations show that 3D balanced point vortices display interesting and important phenomena.