Penetration of Rotating Convection

A simplified model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale with Rossby number as well as with thermal and viscous diffusivities. Integrating the convection model into a linearization of the dynamics in the transition region between convectively unstable and stably-stratified region yields a Rossby number, diffusivity, and pressure scale height dependent convective penetration depth into the stable region. This may have important consequences for mixing along the evolution of rotating stars.