Quareni, F. and Righi, P. (1999) The onset of thermal convection in an infinite Prandtl number, variable viscosity, compressible Earth's mantle by the meanfield approximation. Il nuovo cimento C, 22 C (2). pp. 165180. ISSN 18269885

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Abstract
The values of the Rayleigh number critical for the onset of Thermal instability in an infinite Prandtl number, compressible Earth’s mantle are determined against the aspect ratio (the ratio between the width and the depth of the cell) for constant and for pressure and temperaturedependent viscosity. The procedure adopted follows the experimental approach which determines the critical Rayleigh number as the value at which the heat flux across the fluid exceeds the conductive one. We solve the singlemode meanfield equations for the conservation of mass, momentum and energy and evaluate the Nusselt number, i.e. the ratio between the actual heat transfer and the heat which would be transported only by conduction. The value of the Rayleigh number for which the Nusselt number exceeds unity can be identified as the critical value. Between incompressible and compressible fluids with constant viscosity the critical Rayleigh numbers differ at most by 10–20% for cells aspect ratios between 0.1 to about 30, while at larger aspect ratios compressibility yields critical Rayleigh numbers one or more orders of magnitude larger. For variable viscosity, since a more viscous interior prevents motion, a much higher Rayleigh number is required for the onset of convection. It is also shown how viscous dissipation of heat increases the critical Rayleigh number, while compressibility favours the onset of convection.
Item Type:  Article 

Uncontrolled Keywords:  Structure of the crust and upper mantle; convection and heat transfer; convection currents 
Subjects:  500 Scienze naturali e Matematica > 550 Scienze della Terra > 551 Geologia, Idrologia, Meteorologia > 551.1 Struttura generale e proprietà della Terra > 551.11 Interno della Terra 
Depositing User:  Marina Spanti 
Date Deposited:  28 May 2018 14:15 
Last Modified:  28 May 2018 14:15 
URI:  http://eprints.bice.rm.cnr.it/id/eprint/13150 
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