The effect of a radial magnetic field on the stability of Couette flow through narrow-gap

Abstract

<span style="font-size: 13.5pt;mso-bidi-font-size:8.5pt;font-family:" times="" new="" roman","serif""="">The linear stability of Couette flow in a narrow-gap of two concentric cylinders with either the inner one rotating or both counter-rotating, and in the presence of a radial magnetic field is reported here. The eigenvalue problem is solved numerically by a finite-difference technique. The radial velocity perturbation and the cell-patterns at the onset of instability are shown graphically. It is observed that the maximum of the radial velocity perturbation is found to shift increasingly towards the inner cylinder whereas the cells are found to elongate increasingly in the radial direction and get reduced very much in the axial direction which is exactly opposite to that observed in the presence of an axial magnetic field. Numerical values of the critical wave number <i>a</i><i>_{<span style="font-size:14.0pt; mso-bidi-font-size:9.0pt;font-family:" times="" new="" roman","serif""="">c</span>}</i><i><span style="font-size:14.0pt;mso-bidi-font-size:9.0pt;font-family:" times="" new="" roman","serif""=""> </span></i><span style="font-size:13.5pt;mso-bidi-font-size:8.5pt;font-family: " times="" new="" roman","serif""="">and the critical Taylor number <i><span style="font-size:14.0pt;mso-bidi-font-size:9.0pt;font-family:" times="" new="" roman","serif""="">T_c </span></i><span style="font-size:13.5pt;mso-bidi-font-size:8.5pt;font-family: " times="" new="" roman","serif""="">are also listed.

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