  Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple
equilibrium states as a consequence of bottom topography in their pioneering
work on the quasi-geostrophic barotropic flow over topography in a
$\beta$-plane channel. In the present paper, we prove that the basic flow is
asymptotically stable in a parameter region, including the flat topography
situation, which excludes the existence of multiple equilibrium states therein.
Moreover, we show that an additional condition on the average zonal force or
the average zonal velocity is indispensable to the well-posedness of the
Charney-DeVore quasi-geostrophic equation. Coexistence of at least three
equilibrium states is confirmed by a pseudo-arclength continuation method for
different topographic amplitudes. The stabilities of the equilibrium states are
examined by high-resolution direct numerical simulations.
