  In commonly used formulations of the Boussinesq approximation centrifugal
buoyancy effects related to differential rotation, as well as strong vortices
in the flow, are neglected. However, these may play an important role in
rapidly rotating flows, such as in astrophysical and geophysical applications,
and also in turbulent convection. We here provide a straightforward approach
resulting in a Boussinesq-type approximation that consistently accounts for
centrifugal effects. Its application to the accretion-disk problem is
discussed. We numerically compare the new approach to the typical one in fluid
flows confined between two differentially heated and rotating cylinders. The
results justify the need of using the proposed approximation in rapidly
rotating flows.
