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Kinematic dynamo and intermittence in a turbulent flow

Abstract The large time asymptotics of a magnetic field in a turbulent δ-correlated (in time) flow of an ideal incompressible fluid are studied. It is shown that the magnetic field exhibits the dynamo effect (exponential stretching) unless the Lagrangian flow generated by the velocity field is (almost surely) distance preserving; and it is intermittent unless the Lagrangian flow associated to the turbulent component of the velocity is (almost surely) distance preserving.