Journal of Fluid Mechanics


Vortex dynamos

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] 


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)