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Localised rotating convection induced by topography


Bassom, AP and Soward, AM, Localised rotating convection induced by topography, Physica D: Nonlinear Phenomena, 97, (1-3) pp. 29-44. ISSN 0167-2789 (1996) [Refereed Article]

DOI: doi:10.1016/0167-2789(96)00149-2


The onset of instability of a rapidly rotating, self-gravitating, Boussinesq fluid in a spherically symmetric cavity containing a uniform distribution of heat sources in the small Ekman number limit (E ⪡ 1) is characterised by the longitudinal propagation of thermal Rossby waves on a short azimuthal φ-length scale O(E1/3). Here we investigate the onset of instability via a steady geostrophic mode of convection which may occur when the outer spherical boundary is deformed. Attention is restricted to topographic features with simple longitudinal dependence proportional to cos and small height of order ε / 𝑚. Motion is composed of two parts: the larger is geostrophic and follows the geostrophic contours; the smaller is convective and locked to the topography. Analytic solutions are obtained for the case of rigid boundaries when E1/2 ⪡ ε ⪡ 1 and E1/8 ⪡ 𝑚 ⪡ E1/3; onset of instability is characterised by these modes (with geostrophic motion localised radially on a length scale O(E1/8) when ε2E2/3𝑚3/2. Solutions are obtained for the case of slippery boundaries in different parameter ranges and, in contrast, these are not localised but fill the sphere. In both cases the critical Rayleigh number grows with decreasing ε, localising the convection of heat in a neighbourhood close to the surface.

Item Details

Item Type:Refereed Article
Keywords:rotating convection, geostrophy, topography
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108050
Year Published:1996
Web of Science® Times Cited:4
Deposited By:Mathematics and Physics
Deposited On:2016-04-05
Last Modified:2016-07-08

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