Journal of Fluid Mechanics



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Vortex dynamos


STEFAN G. LLEWELLYN SMITH a1 and S. M. TOBIAS a2
a1 Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA
a2 Department of Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK

Article author query
smith s   [Google Scholar] 
tobias s   [Google Scholar] 
 

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 $2 \frac{1}{2}$-dimensional velocity field of the form $\left(u(x,y,t),v(x,y,t),w(x,y,t)\right)$ 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 $\Rey$ and magnetic Reynolds number $\Rem$, but the flow continues to act as a dynamo for large $\Rey$ and $\Rem$. Moreover the dynamo is still efficient even in the limit $\Rey \,{\gg}\, \Rem$, providing $\Rem$ is large enough, because of the formation of coherent structures.

(Received August 14 2002)
(Revised March 7 2003)



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