  A monomodal model for stellar and planetary convection is derived for the
magnitude of the rms velocity, degree of superadiabaticity, and characteristic
length scale as a function of rotation rate as well as with thermal and viscous
diffusivities. The convection model is used as a boundary condition for a
linearization of the equations of motion in the transition region between
convectively unstable and stably-stratified regions, yielding the depth to
which convection penetrates into the stable region and establishing a
relationship between that depth and the local convective Rossby number,
diffusivity, and pressure scale height of those flows. Upward and downward
penetrative convection have a similar scaling with rotation rate and
diffusivities, but they depend differently upon the pressure scale height due
to the differing energetic processes occurring in convective cores of
early-type stars versus convective envelopes of late-type stars.
