Temperature and heat flux scalings for isoviscous thermal convection in spherical geometry

Details Temperature and heat flux scalings for isoviscous thermal convection in spherical geometry Temperature and heat flux scalings for isoviscous thermal convection in spherical geometry

Dec 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufm.p41a..05d&link_type=abstract

American Geophysical Union, Fall Meeting 2009, abstract #P41A-05

Physics

[5724] Planetary Sciences: Fluid Planets / Interiors, [8121] Tectonophysics / Dynamics: Convection Currents, And Mantle Plumes, [8147] Tectonophysics / Planetary Interiors

Scientific paper

Reconstruction of the thermal history of planetary mantles requires, in particular, a good description of the heat flux that can be transported through planetary mantles. A convenient way to quantify heat flux, internal temperature and other important observables, is to build appropriate scaling relationships, which relate these observables to controlling parameters. Scaling relationships strongly depend on the system physical (geometry, boundary conditions, mode of heating) and rheological properties. A key ingredient that has recently been incorporated in convection models is a realistic, spherical geometry. Using STAGYY, we performed two series (one for bottom heating, the other for mixed heating) of numerical experiments of thermal convection for an isoviscous fluid in spherical geometry. We then invert our results for scaling relationships for both the heat flux and the internal temperature. In the case of bottom heating, the internal temperature depends only on the curvature, but does not fit the relationship predicted thermal boundary layer analysis. Heat transfer efficiency decreases as curvature increases. The Nusselt number is a power law of both the Rayleigh number and the internal temperature, and the Rayleigh number exponent slightly depends on the curvature. In the case of mixed heating, the internal temperature is a weighted sum of the temperatures derived for bottom heating and for internal heating. The Nusselt number is described by a scaling similar to that found in the bottom heating case, but with different parameter values. Finally, we use our scaling relationships to calculate various thermal evolution models. Additional complexities of planetary mantles include temperature dependent viscosity and the presence of chemical heterogeneities. A more realistic description of the thermal history of planetary mantles thus requires scaling relationships that account for these parameters, which we will consider in future steps.

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