Point-vortex dynamics in three-dimensional ageostrophic balanced flows

Abstract

Geophysical turbulent flows, characterized by rapid rotation, quantified by small Rossby number, and stable stratification, often self-organize into a collection of coherent vortices, referred to as a vortex gas. The lowest-order asymptotic expansion in Rossby number is quasigeostrophy, which has purely horizontal velocities and cyclone–anticyclone antisymmetry. Ageostrophic effects are important components of many geophysical flows and, as such, these phenomena are not well modelled by quasigeostrophy. The next-order correction in Rossby number, which includes ageostrophic effects, is the so-called balanced dynamics. Balanced dynamics includes ageostrophic vertical velocity and breaks the geostrophic cyclone–anticyclone antisymmetry. Point-vortex solutions are well known in two-dimensional and quasigeostrophic dynamics and are useful for studying the vortex-gas regime of geophysical turbulence. Here, we find point-vortex solutions in fully three-dimensional continuously stratified QG $^{+1}$ dynamics, a particular formulation of balanced dynamics. Simulations of QG $^{+1}$ point vortices show several interesting features not captured by quasigeostrophic point vortices including significant vertical transport on long time scales. The ageostrophic component of QG $^{+1}$ point vortex point-vortex dynamics renders them useful in modelling flows where quasigeostrophy filters out important physical processes.