Hydrothermal Convection in Moderately Thin Spherical Shells

Zhifeng Dai, Keke Zhang, Xinhao Liao, and Gerald Schubert
Phys. Rev. Lett. 101, 028501 – Published 8 July 2008

Abstract

Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.

  • Figure
  • Received 25 March 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.028501

©2008 American Physical Society

Authors & Affiliations

Zhifeng Dai1, Keke Zhang1, Xinhao Liao2, and Gerald Schubert3

  • 1Department of Mathematical Sciences, University of Exeter, EX4 4QE, United Kingdom
  • 2Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
  • 3Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, USA

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Issue

Vol. 101, Iss. 2 — 11 July 2008

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