arXiv subjects

R. J. West

Publications and source records attributed to R. J. West.

3 recordsLinked to original sources

arXiv2003

Small-scale turbulent dynamo - a numerical investigation

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.

astro-ph↗

arXiv2003

Analytical solution for nonlinear Schrodinger vortex reconnection

Analysis of the nonlinear Schrodinger vortex reconnection is given in terms of coordinate-time power series. The lowest order terms in these series correspond to a solution of the linear Schrodinger equation and provide several interesting properties of the reconnection process, in particular the non-singular character of reconnections, the anti-parallel configuration of vortex filaments and a square-root law of approach just before/after reconnections. The complete infinite power series represents a fully nonlinear analytical solution in a finite volume which includes the reconnection point, and is valid for finite time provided the initial condition is an analytic function. These series solutions are free from the periodicity artifacts and discretization error of the direct computational approaches and they are easy to analyze using a computer algebra program.

physics.flu-dyn↗

arXiv2003

Fourier space intermittency of the small-scale turbulent dynamo

The small-scale turbulent dynamo in the high Prandtl number regime is described in terms of the one-point Fourier space correlators. The second order correlator of this kind is the energy spectrum and it has been previously studied in detail. We examine the higher order k-space correlators which contain important information about the phases of the magnetic wavepackets and about the dominant structures of the magnetic turbulence which cause intermittency. In particular, the fourth-order correlators contain information about the mean-square phase difference between any two components of the magnetic field in a plane transverse to the wavevector. This can be viewed as a measure of the magnetic field's polarization. Examining this new quantity, the magnetic field is shown to become plane polarized in the Kazantsev-Kraichnan model at large time, corresponding to a strong deviation from Gaussianity. We derive a closed equation for the generating function of the Fourier correlators and find the large-time asymptotic solutions of these correlators at all orders. The time scaling of these solutions implies the magnetic field has log-normal statistics, whereas the wavenumber scaling indicates that the field is dominated by intermittent fluctuations at high k.

astro-ph↗