Article

Hydrothermal convection in moderately thin spherical shells.

Department of Mathematical Sciences, University of Exeter, EX4 4QE, United Kingdom.
Physical Review Letters (impact factor: 7.37). 08/2008; 101(2):028501.
Source: PubMed

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.

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Keywords

13-fold mathematical degeneracy
 
analytical solutions
 
degeneracy
 
different three-dimensional analytical solutions
 
direct numerical simulation
 
nonlinear effect
 
numerical simulations
 
perturbation analysis
 
pore water
 
satisfactory agreement
 
simulation
 
thin spherical shell
 

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