This chapter examines the effects of rotation on convection and gravity waves. Flows in the atmospheres, oceans, and liquid cores of terrestrial planets are dominated by the Coriolis forces, as are the interiors of giant planets and stars. The sum of gravitational and centrifugal forces can go to zero at the top boundary of a rapidly rotating star or accretion disk. The time rate of change of the planetary rotation rate gives rise to Poincaré forces. The chapter first considers Coriolis, centrifugal, and Poincaré forces before explaining the modifications needed to add these effects of rotation to previous models of convection and gravity waves in 2D cartesian box and cylindrical annulus geometries, both of which now lie within a rotating equatorial plane. It also describes 2.5D rotating models and 3D spherical-shell magnetohydrodynamic dynamo models.
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