# A model of rotating convection in stellar and planetary interiors: I - convective penetration

## TL;DR

This paper develops a model for stellar and planetary convection that predicts how convection properties and penetration depth depend on rotation rate, diffusivities, and stellar structure, providing insights into convective boundary dynamics.

## Contribution

It introduces a monomodal convection model linking velocity, superadiabaticity, and length scale to rotation and diffusivities, and relates convective penetration depth to local flow parameters.

## Key findings

- Convection velocity and superadiabaticity scale with rotation rate and diffusivities.
- Penetration depth depends on the Rossby number, diffusivities, and pressure scale height.
- Upward and downward penetration exhibit similar but distinct scaling behaviors.

## Abstract

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.