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Vortex dynamos

By S.G. Llewellyn Smith and S.M. Tobias

Abstract

We investigate the kinematic dynamo properties of interacting vortex tubes. These flows are of great importance in geophysical and astrophysical fluid dynamics: for a large range of systems, turbulence is dominated by such coherent structures. We obtain a dynamically consistent 2(2)-(1)-dimensional velocity field of the form (u(x, y, t), upsilon(x, y, t), w(x, y, t)) by solving the z-independent Navier-Stokes equations in the presence of helical forcing. This system naturally forms vortex tubes via an inverse cascade. It has chaotic Lagrangian properties and is therefore a candidate for fast dynamo action. The kinematic dynamo properties of the flow are calculated by determining the growth rate of a small-scale seed field. The growth rate is found to have a complicated dependence on Reynolds number Re and magnetic Reynolds number Rm, but the flow continues to act as a dynamo for large Re and Rm. Moreover the dynamo is still efficient even in the limit Re much greater than Rm, providing Rm is large enough, because of the formation of coherent structures

Publisher: Cambridge University Press
Year: 2004
OAI identifier: oai:eprints.whiterose.ac.uk:1272

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