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Microwave-heating laboratory experiments for planetary mantle convection

Published online by Cambridge University Press:  15 July 2015

A. Limare ,
K. Vilella ,
E. Di Giuseppe ,
C. G. Farnetani ,
E. Kaminski ,
E. Surducan ,
V. Surducan ,
C. Neamtu ,
L. Fourel  and
C. Jaupart
A. Limare*
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
K. Vilella
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
E. Di Giuseppe
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France CEMEF, MINES ParisTech, CNRS, CS 10207, 06904 Sophia Antipolis, France
C. G. Farnetani
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
E. Kaminski
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
E. Surducan
Affiliation:
National Institute for Research and Development of Isotopic and Molecular Technologies, 67-103 Donath St., 400293 Cluj-Napoca, Romania
V. Surducan
Affiliation:
National Institute for Research and Development of Isotopic and Molecular Technologies, 67-103 Donath St., 400293 Cluj-Napoca, Romania
C. Neamtu
Affiliation:
National Institute for Research and Development of Isotopic and Molecular Technologies, 67-103 Donath St., 400293 Cluj-Napoca, Romania
L. Fourel
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
C. Jaupart
Affiliation:
Institut de Physique du Globe de Paris, Université Paris Diderot, CNRS, 1 rue Jussieu, 75238 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

Thermal evolution of telluric planets is mainly controlled by secular cooling and internal heating due to the decay of radioactive isotopes, two processes that are equivalent from the standpoint of convection dynamics. In a fluid cooled from above and volumetrically heated, convection is dominated by instabilities of the top boundary layer and the interior thermal structure is non-isentropic. Here we present innovative laboratory experiments where microwave radiation is used to generate uniform internal heat in fluids at high Prandtl number (${>}300$) and high Rayleigh–Roberts number (ranging from $10^{4}$ to $10^{7}$), appropriate for planetary mantle convection. Non-invasive techniques are employed to determine both temperature and velocity fields. We successfully validate the experimental results by conducting numerical simulations in three-dimensional Cartesian geometry that reproduce the experimental conditions. Scaling laws relating key characteristics of the thermal boundary layer, namely its thickness and temperature drop, to the Rayleigh–Roberts number have been established for both rigid and free-slip boundary conditions. A robust conclusion is that for rigid boundary conditions the internal temperature is significantly higher than for free-slip boundary conditions. Our scaling laws, coupled with plausible physical parameters entering the Rayleigh–Roberts number, enable us to calculate the mantle potential temperature for the Earth and Venus, two telluric planets with different mechanical boundary conditions at their surface.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Mantle convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 50 - 67
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© 2015 Cambridge University Press 

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