Equatorially Trapped Convection in a Rapidly Rotating Shallow Shell
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.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.10293
 Bibcode:
 2018arXiv180410293B
 Keywords:

 Physics  Fluid Dynamics;
 Physics  Geophysics
 EPrint:
 26 pages, 10 figures. Accepted for publication in Physical Review Fluids