Small-scale turbulent dynamo - a numerical investigation

Abstract

We present the results of a numerical investigation of the turbulent kinematic dynamo problem in a high Prandtl number regime. The scales of the magnetic turbulence we consider are far smaller than the Kolmogorov dissipative scale, so that the magnetic wavepackets evolve in a nearly smooth velocity field. Firstly, we consider the Kraichnan-Kazantsev model (KKM) in which the strain matrix is taken to be independent of coordinate and Gaussian white in time. To simulate the KKM we use a stochastic Euler-Maruyama method. We test the theoretical predictions for the growth of rates of the magnetic energy and higher order moments (Kazantsev, 1968; Kulsrud & Anderson, 1992; Chertkov et al., 1999), the shape of the energy spectrum (Kazantsev, 1968; Kulsrud & Anderson, 1992; Schekochihin et al., 2000a; Nazarenko et al., 2003) and the behaviour of the polarisation and spectral flatness Nazarenko et al., 2003). In general, the results appear to be in good agreement with the theory, with the exception that the predicted decay of the polarisation in time is not reproduced well in the stochastic numerics. Secondly, in order to study the sensitivity of the KKM predictions to the choice of strain statistics, we perform additional simulations for the case of a Gaussian strain with a finite correlation time and also for a strain taken from a DNS data set. These experiments are based on non-stochastic schemes, using a timestep that is much smaller than the correlation time of the strain. We find that the KKM is generally insensitive to the choice of strain statistics and most KKM results, including the decay of the polarisation, are reproduced well. The only exception appears to be the flatness whose spectrum is not reproduced in accordance with the KKM predictions in these simulations.