General theory of random fast dynamos

Establish a general theory showing that suitable random velocity fields satisfying an appropriate non-degeneracy condition are fast dynamos, meaning that their associated magnetic induction equations exhibit exponential magnetic-field growth uniformly for sufficiently small resistivities.

Background

The paper constructs one particular smooth random fast dynamo on the three-dimensional torus by using alternating, randomly translated velocity pulses and a special tridiagonal Fourier-space structure. The authors contrast this bespoke construction with the broader goal of identifying general conditions under which random flows produce dynamo action.

Randomness is expected to help by preventing cancellations that can otherwise erase mechanisms producing exponential growth. The unresolved problem is to prove that this effect holds in a general setting, rather than only for the specially designed algebraic example developed in the paper.