(1) Department of Geology, Colby
College, Waterville, ME USA
(2) Department of Geophysics,
Faculty of Mathematics and Physics, Charles University, Prague, Czech
Republic
(3) Department of Geology and
Geophysics and Minnesota Supercomputing
Institute, University of Minnesota, MN USA
More than twenty years ago, Skilbeck and Whitehead (1978) proposed on the basis of laboratory experiments that secondary instabilities can develop from low Reynolds number flow due to the interaction between a background shear flow and a bent upwelling. This scenario, involving the ejection of a Rayleigh-Taylor secondary instability from the bent plume, was used to explain the hotspots associated with the Hawaiian-Emperor island chain. We have studied with an axisymmetric spherical-shell numerical code using higher-order finite-differences high Rayleigh number convection spanning from one million to ten billion with grids up to around two million points. We find that within a critical window in Rayleigh number space, between around ten million and a few billion, that secondary instabilities in the form of folding and the formation of narrow-looped structures can develop from a primary upwelling. At times, several of these narrow secondary upwellings can be formed along one primary upwelling, similar in morphology to those found in the Whitehead experiments There is a spectrum of wavelengths within which these instabilities are formed and we found the spectrum to vary between 0.1 and 0.5 of the layer thickness with the average wavelength being 0.3. Our results on the spacing of the wavelengths of these secondary instabilities and the range of Rayleigh number they are formed would argue for an upper-mantle theatre in which these instabilities would develop with an upper-mantle viscosity between 10^18 Pa s to around 5x10^19 Pa s.
Not available.
References
[1] Skilbeck, J.N.and J.A. Whitehead, Formation of discrete islands in linear
chains, Nature, Vol. 272, pp. 499-501, 1978.