Advection of vector fields by chaotic flows

Details Advection of vector fields by chaotic flows Advection of vector fields by chaotic flows

1993-07-26

arxiv.org/abs/chao-dyn/9307011v1

Annals of New York Academy of Sciences 706, 148 (1993)

Physics

Condensed Matter

12 pages, Latex. Ask for figures from vattay@nbivax.nbi.dk

Scientific paper

10.1111/j.1749-6632.1993.tb24687

We have introduced a new transfer operator for chaotic flows whose leading eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied cycle expansion of the Fredholm determinant of the new operator to evaluation of its spectrum. The theory hs been tested on a normal form model of the vector advecting dynamical flow. If the model is a simple map with constant time between two iterations, the dynamo rate is the same as the escape rate of scalar quantties. However, a spread in Poincar\'e section return times lifts the degeneracy of the vector and scalar advection rates, and leads to dynamo rates that dominate over the scalar advection rates. For sufficiently large time spreads we have even found repellers for which the magnetic field grows exponentially, even though the scalar densities are decaying exponentially.

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