Equatorially Trapped Convection in a Rapidly Rotating Shallow Shell

TL;DR

This paper investigates equatorially trapped convection in rapidly rotating shallow shells, revealing how the trapping parameter controls convection extent and vigor, supported by DNS and an asymptotic model, advancing understanding of planetary subsurface ocean dynamics.

Contribution

It introduces a nonhydrostatic equatorial $eta$-plane convection model that accurately captures convection trapping, offering a new theoretical framework for nonlinear studies in planetary science.

Findings

Convection is trapped near the equator at low latitudes.

The trapping parameter $eta$ governs convection extent and strength.

The asymptotic model reproduces DNS results at lower computational cost.

Abstract

Motivated by the recent discovery of subsurface oceans on planetary moons and the interest they have generated, we explore convective flows in shallow spherical shells of dimensionless gap width $\varepsilon^2\ll 1$ in the rapid rotation limit $\mathrm{E}\ll1$, where $\mathrm{E}$ is the Ekman number. We employ direct numerical simulations (DNS) of the Boussinesq equations to compute the local heat flux $\mathrm{Nu}(\lambda)$ as a function of the latitude $\lambda$ and use the results to characterize the trapping of convection at low latitudes, around the equator. We show that these results are quantitatively reproduced by an asymptotically exact nonhydrostatic equatorial $\beta$-plane convection model at a much more modest computational cost than DNS. We identify the trapping parameter $\beta=\varepsilon \mathrm{E}^{-1}$ as the key parameter that controls the vigor and latitudinal extent of convection for moderate thermal forcing when $\mathrm{E}\sim\varepsilon$ and $\varepsilon\downarrow 0$. This model provides a new theoretical paradigm for nonlinear investigations.