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A buoyant flow structure in a magnetic field: Quasi-steady states and linear-nonlinear transitions

Sreenivasan, B. (2008) A buoyant flow structure in a magnetic field: Quasi-steady states and linear-nonlinear transitions. Physics Letters A, 372 (33). pp. 5471-5478. ISSN 0375-9601

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Abstract

The confined evolution of a buoyant blob of fluid subject to a vertical magnetic field is investigated in the limit of low magnetic Reynolds number. When the applied magnetic field is strong, the rise velocity of the blob is small. As the vorticity diffuses along the magnetic field lines, a quasi-steady state characterised by a balance between the work done by buoyancy and Ohmic dissipation is eventually reached at time tqs(L2/δ2)τ, where L is the axial dimension of the fluid domain, δ is the radius of the buoyant blob and τ is the magnetic damping time. However, when the applied magnetic field is weak or the axial length is sufficiently large compared to the blob size, the growth of axial velocity eventually makes the advection of vorticity significant. The typical time for the attainment of this nonlinear phase is , where N0 is the magnetic interaction parameter at time t=τ. The order-of-magnitude estimates for the timescales tqs and tnl are verified by computational experiments that capture both the linear and nonlinear phases.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Elsevier B.V. This is an author produced version of a paper published in Physics Letters A. Uploaded in accordance with the publisher's self archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 03 Oct 2008 13:24
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1016/j.physleta.2008.06.075
Status: Published
Publisher: Elsevier B.V.
Refereed: Yes
Identification Number: 10.1016/j.physleta.2008.06.075
URI: http://eprints.whiterose.ac.uk/id/eprint/4728

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