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Hydromagnetic Flow in a Wall Heated Rigid Rotating Annulus
Author(s) -
Vempaty S.,
Satyamurty P.,
Balasubramanian R.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200004)80:4<273::aid-zamm273>3.0.co;2-l
Subject(s) - annulus (botany) , mechanics , flow (mathematics) , physics , materials science , geology , classical mechanics , composite material
Linear, steady, axisymmetric flow of an electrically conducting homogeneous fluid confined within a rapidly rotating rigid annulus and caused by a horizontally applied temperature gradient, is investigated under the assumptions of small thermal Rossby number, small Ekman number, and small magnetic Reynolds number. The applied magnetic field and the rotation vector are aligned normal to the horizontal boundaries. The dynamics of the inviscid interior and the vertical boundary layers are analyzed as functions of the rotational magnetic interaction parameter α 2 (= σB 2 /2 ρΩ ) under the assumption that the transfer of heat is purely conductive. If α 2 ≪ 1 the flow behaves as a nonmagnetic rotational flow to dominant order, and if α 2 ≫ E —1/3 it behaves as a strongly magnetic nonrotational flow. In the intermediate range 1 ≪ α 2 ≪ E —1/3 , the baroclinicity of the interior induces a meridional electric current circulation of O (1/ α 4 ) which in turn induces a meridional circulation of mass flux O (1/ α 2 ). These circulations are confined to the interior and inviscid magnetic α —2 regions. The E 1/3 layer arises to adjust the azimuthal velocity of O (1) of the inviscid region to zero at the sidewall. These two vertical layers together support higher order circulations of mass flux O ( E 1/2 / α ) and O ( E 1/2 / α 3 ) while the lowest order circulation of mass flux O ( E 1/3 ) occurs only in E 1/3 layer. A magnetic inviscid E 1/3 sublayer with an axial scale O ( α 2 E 1/3 ) is found to exist at the top and bottom plates to provide smooth passage to electric currents between the Ekman‐Hartmann layers and the α —2 layers. The Hadley type circulations for mass and electric current fluxes become very weak.