A dynamo theorem

Abstract

Abstract It is shown that the frozen-in magnetic field in a given random homogeneous flow of an incompressible fluid which is renewed after a finite characteristic time grows exponentially. The rate-of-growth is positive in the limit of small magnetic diffusivity and continuous in v m . The increase of the rates-of-growth for successive field moments is revealed by the intermittent distribution of the magnetic field generated. The results are obtained by reducing the kinematic dynamo problem to the evaluation of the product of a large number of independent random operators.