Secondary upwelling instabilities developed in high Rayleigh number convection: Possible applications to hot spots

(1) Department of Geology, Colby College, Waterville, ME USA
(2) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
(4) Department of Geology and Geophysics and Minnesota Supercomputing Institute, University of Minnesota, MN USA

Abstract

We have conducted numerical experiments for mantle convection in an axisymmetrical spherical-shell geometry from Rayleigh numbers ranging from three million to 10 billion for a purely basal heating configuration. We focus on the development of secondary instabilities developed from plumes and compare them with laboratory experiments by Skilbeck and Whitehead (1978) and Whitehead, (1982). For Rayleigh numbers between around thirty million to one billion, a string of these secondary instabilities can develop from a single plume. Analysis of the spectrum of wavelength associated with the fold instabilities shows that there is a window in the Rayleigh number between around ten million and one bilion where these secondary folding instabilities would develop. These results, when applied to the upper mantle, may explain the formation of hot-spots in a turbulently convecting upper-mantle with a Rayleigh number greater than ten million.

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References
[1] Skilbeck, J.N. and Whitehead J.A., Formation of discrete islands in linear chains, Nature, Vol. 272, pp. 499-501, 1978.
[2] Whitehead, J.A., Instabilities of fluid conduits in a flowing earth -- are plates lubricated by the asthenosphere, Geophys J. R. Astron. Soc., Vol. 70, pp. 415-433, 1982.