Here, we find point-vortex solutions in fully three-dimensional continuously stratified QG $^$$ Point-vortex solutions are well known in two-dimensional and quasigeostrophic dynamics and are useful for studying the vortex-gas regime of geophysical turbulence.
Balanced dynamics includes ageostrophic vertical velocity and breaks the geostrophic cyclone–anticyclone antisymmetry. The next-order correction in Rossby number, which includes ageostrophic effects, is the so-called balanced dynamics. Ageostrophic effects are important components of many geophysical flows and, as such, these phenomena are not well modelled by quasigeostrophy. The lowest-order asymptotic expansion in Rossby number is quasigeostrophy, which has purely horizontal velocities and cyclone–anticyclone antisymmetry. 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.
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