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

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.
Comment: 12 pages