Suppression of small-scale dynamo in time irreversible turbulence

The conventional theory of small-scale magnetic field generation in a turbulent flow considers time-reversible random flows. However, real turbulent flows are known to be time irreversible: the presence of energy cascade is an intrinsic property of turbulence. We generalize the 'standard' model to account for the irreversibility. We show that even small time asymmetry leads to significant suppression of the dynamo effect at low magnetic Prandtl numbers, increases the generation threshold and may even make generation impossible for any magnetic Reynolds number. We calculate the magnetic energy growth rate as a function of the parameters of the flow.