  We study thermal convection in a rotating fluid in order to better understand
the properties of convection zones in rotating stars and planets. We first
derive mixing-length theory for rapidly-rotating convection, arriving at the
results of Stevenson (1979) via simple physical arguments. The theory predicts
the properties of convection as a function of the imposed heat flux and
rotation rate, independent of microscopic diffusivities. In particular, it
predicts the mean temperature gradient; the rms velocity and temperature
fluctuations; and the size of the eddies that dominate heat transport. We test
all of these predictions with high resolution three-dimensional hydrodynamical
simulations of Boussinesq convection in a Cartesian box. The results agree
remarkably well with the theory across more than two orders of magnitude in
rotation rate. For example, the temperature gradient is predicted to scale as
the rotation rate to the 4/5th power at fixed flux, and the simulations yield
$0.75\pm 0.06$. We conclude that the mixing length theory is a solid foundation
for understanding the properties of convection zones in rotating stars and
planets.
