Equatorially trapped convection in a rapidly rotating shallow shell

Benjamin Miquel, Jin-Han Xie, Nicholas Featherstone, Keith Julien, and Edgar Knobloch
Phys. Rev. Fluids 3, 053801 – Published 16 May 2018

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 ɛ21 in the rapid rotation limit E1, where E is the Ekman number. We employ direct numerical simulation (DNS) of the Boussinesq equations to compute the local heat flux Nu(λ) as a function of the latitude λ 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 β-plane convection model at a much more modest computational cost than DNS. We identify the trapping parameter β=ɛE1 as the key parameter that controls the vigor and latitudinal extent of convection for moderate thermal forcing when Eɛ and ɛ0. This model provides a theoretical paradigm for nonlinear investigations.

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  • Received 22 September 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.053801

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Benjamin Miquel1,*, Jin-Han Xie2, Nicholas Featherstone1, Keith Julien1,†, and Edgar Knobloch3

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
  • 3Department of Physics, University of California, Berkeley, California 94720, USA

  • *benjamin.miquel@colorado.edu
  • julien@colorado.edu

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Issue

Vol. 3, Iss. 5 — May 2018

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