# The stability of vortices in gas on the $l$-plane: the influence of centrifugal force

## TL;DR

This paper demonstrates that including centrifugal force in the $l$-plane atmospheric model significantly affects vortex stability, eliminating stable vortex solutions and providing a special integrable case for one-atomic gases.

## Contribution

It introduces the impact of centrifugal force into the $l$-plane vortex stability analysis and identifies conditions where the system becomes integrable.

## Key findings

- Centrifugal force drastically reduces vortex stability.
- Stable vortices disappear when centrifugal force is considered.
- The system is integrable for $\gamma=2$ in a special case.

## Abstract

We show that a small correction due to centrifugal force usually neglected in the $l$-plane model of atmosphere drastically influences on the stability of vortices. Namely, in the presence of the Coriolis force only there exists a wide range of parameter ensuring nonlinear stability of a vortex with uniform deformation. Taking into account the centrifugal force results in a disappearance of stable vortices in the above-mentioned class of motions. We also prove that for the heat ratio $\gamma=2$, corresponding to the one-atomic gas, the system of equations, describing the gas on the $l$-plane with the correction due to centrifugal force can be integrated in a special case.