  We predict and describe a new collective mode in rotating Bose-Einstein
condensates, which is very similar to the Rossby waves in geophysics. In the
regime of fast rotation, the Coriolis force dominates the dynamics and acts as
a restoring force for acoustic-drift waves along the condensate. We derive a
nonlinear equation that includes the effects of both the zero-point pressure
and the anharmonicity of the trap. It is shown that such waves have negative
phase speed, propagating in the opposite sense of the rotation. We discuss
different equilibrium configurations and compare with those resulting from the
Thomas-Fermi approximation.
