  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.
