Finite-correlation-time effects in the kinematic dynamo problem

Most of the theoretical results on the kinematic amplification of small-sca le magnetic fluctuations by turbulence have been confined to the model of w hite-noise-like (delta -correlated in time) advecting turbulent velocity fi eld. In this work, the statistics of the passive magnetic field in the diff usion-free regime are considered for the case when the advecting flow is fi nite-time correlated. A new method is developed that allows one to systemat ically construct the correlation-time expansion for statistical characteris tics of the field such as its probability density function or the complete set of its moments. The expansion is valid provided the velocity correlatio n time is smaller than the characteristic growth time of the magnetic fluct uations. This expansion is carried out up to first order in the general cas e of a d-dimensional arbitrarily compressible advecting flow. The growth ra tes for all moments of the magnetic-field strength are derived. The effect of the first-order corrections due to the finite correlation time is to red uce these growth rates. It is shown that introducing a finite correlation t ime leads to the loss of the small-scale statistical universality, which wa s present in the limit of the delta -correlated velocity field. Namely, the shape of the velocity time-correlation profile and the large-scale spatial structure of the flow become important. The latter is a new effect, that i mplies, in particular, that the approximation of a locally-linear shear flo w does not fully capture the effect of nonvanishing correlation time. Physi cal applications of this theory include the small-scale kinematic dynamo in the interstellar medium and protogalactic plasmas. (C) 2001 American Insti tute of Physics.