Convection in rotating non-uniformly stratified spherical fluid shells in dependence on Ekman and Prandtl numbers

Abstract

Please cite this article as:Šimkanin, J., Hejda, P., Saxonbergová-Jankovičová, D., Convection in rotating non-uniformly stratified spherical fluid shells in dependence on Ekman and Prandtl numbers, Physics of the Earth and Planetary Interiors (2008), doi:10.1016/j.pepi.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Page 1 of 18A c c e p t e d M a n u s c r i p t We present an investigation of rotating convection in non-uniformly stratified spherical shells in dependence on Prandtl, Ekman and Rayleigh numbers. Attention is focused on the case in which the thickness of both sublayers (stable and unstable) is identical, which was not investigated before. Influence of stratification is more evident at small values of Rayleigh numbers (large values of Ekman numbers), at large Rayleigh numbers is almost negligible. For small Rayleigh numbers in the case of uniform stratification a large-scale columnar convection is developed in the whole volume, in the case of non-uniform stratification it is suppressed to the unstably stratified region but slightly penetrates to the stably stratified one, except the case of large Prandtl numbers when the convection significantly penetrate to the stably stratified region. The spiralling nature of convection is a dominant feature at moderate Prandtl numbers, the strong spiralling is typical at small Prandtl numbers but it disappears at large Prandtl numbers. For large Rayleigh numbers (small values of Ekm developed. The multilayer convection (``teleconvection") is not developed in our case of non-uniform stratification because of the significant amount of stable stratification. Our case is a typical extreme case. It is dissimilar to both cases if the stably stratified sublayer is thinner than the unstably stratified one and if the unstably stratified sublayer is thinner than the stably stratified one.

Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number and stratification

“…Heimpel et al 2005), planetary interiors (e.g. Braginsky 1964; Fearn & Loper 1981; Zhang & Schubert 2000; Šimkanin et al 2003, 2006, 2010; Stanley & Bloxham 2004, 2006; Christensen 2006; Christensen & Wicht 2008; Stanley & Mohammadi 2008), etc.…”

“…Non-uniform stratification can be simulated thermodynamically also in the Boussinesq models by means of internal heat sources (e.g. Zhang & Schubert 2000;Šimkanin et al 2003, 2006, 2010. If the stably stratified sublayer is very thin (for a geometric configuration stable/unstable), then behaviour is close to the case of uniform stratification when the whole layer is unstably stratified.…”

“…Similarly, if the unstably stratified sublayer is very thin, then behaviour is close to the case of uniform stratification when the whole layer is stably stratified. Thus, the effects of non‐uniform stratification are notable if the thicknesses of the stably and unstably stratified sublayers are comparable (Zhang & Schubert 2000; Šimkanin et al 2003, 2006, 2010).…”