Session G10: MHD I

Quantifying the locality/nonlocality of nonlinear interactions in MHD turbulence

The locality functions introduced by Kraichnan give the fraction of the energy flux across a given cutoff wavenumber $k_c$ that is due to nonlinear interactions with wavenumbers k smaller than the cutoff (the infrared locality function) or greater than the cutoff (the ultraviolet locality function). Previous analysis of DNS data for hydrodynamic turbulence (HD) confirmed the theoretical scaling exponent of n=4/3 in the wavenumber ratio $k/k_c$. We have extended the analysis of DNS data to MHD turbulence. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed and the fluxes and locality functions are recovered by partial summations over the relevant shells. Values of 1/3 and 2/3 are found for the scaling exponents of the four individual MHD energy fluxes corresponding to the four nonlinear terms in MHD equations. However, when a sum of two energy conversion terms, among the kinetic and the magnetic energy, is considered instead of its two individual components, its scaling exponent is 2/3, the same as for the remaining two redistribution terms for the kinetic and the magnetic energy. All scaling exponents are smaller than the value of 4/3 found for HD turbulence, indicating significantly more nonlocal character of nonlinear interactions in MHD turbulence.   

Nonlocality and the Critical Reynolds Numbers of the Minimum State Magnetohydrodynamic Turbulence

Magnetohydrodynamic (MHD) systems can be strongly nonlinear (turbulent) when their kinetic and magnetic Reynolds numbers are high, as is the case in many astrophysical and space plasma flows. Unfortunately these high Reynolds numbers are typically much greater than those currently attainable in numerical simulations of MHD turbulence. A natural question to ask is how can researchers be sure that their simulations have reproduced all of the most influential physics of the flows and magnetic fields? In this talk, a metric is defined to indicate whether the necessary physics of interest has been captured. It is found that current computing resources will typically not be sufficient to achieve this minimum state metric.   

Numerical Study for the MHD Homogeneous Decaying Turbulence with the Uniform Magnetic Field

The MHD homogeneous decaying turbulent flows with the uniform magnetic field at three magnetic Prandtl numbers are investigated by means of the direct numerical simulation. The decay of the total energy, which is the sum of the kinetic and magnetic energy, is relaxed due to the additional magnetic field. The anisotropy of the Reynolds and Maxwell normal stresses is not large. However, in the power spectra of the velocity and magnetic fields the small-scale anisotropic property is under the influence of the constant magnetic field. From the viewpoints of the energy spectral budget, the contribution of the energy transformation term related with the mean magnetic field is dominant in comparison with that related with only fluctuating field.   

Turbulent transport of passive scalar in magnetohydrodynamic channel flow

Direct numerical simulations are conducted to analyze transport of a passive scalar in a turbulent flow of an electrically conducting fluid in a channel. Cases of imposed wall-normal, spanwise, and streamwise magnetic field are considered. The magnetic Reynolds and Prandtl numbers are assumed small. The hydrodynamic Reynolds number based on the channel half-width and mean velocity is Re=6000 and the Hartmann number varies from zero to the value slightly below the laminarization threshold. We find that the flow transformation caused by the magnetic field leads to significant changes of the statistical properties of the scalar distribution and of the rate of scalar transport. A particularly important factor is the suppression of turbulent fluctuations of wall-normal velocity in the cases of wall-normal and spanwise magnetic fields.   

Magnetohydrodynamic duct flow at $Re=10^5$ and strong magnetic field

We present the results of high-resolution DNS of the magnetohydrodynamic flows in a duct of square cross-section. The walls of the duct are electrically insulating and the imposed magnetic field is constant, uniform, and parallel to one set of walls. The simulations are performed at the Reynolds number based on the mean velocity and duct half-width $Re=10^5$ and the Hartmann number Ha varying from 0 to 400, i.e. in the range of parameters never before addressed in computational analysis. The numerical model is based on a conservative finite-difference scheme and uses the grid consisting of up to $2048\times 768^2$ points. The results show a sequence of flow regimes that appear with increasing Ha: a turbulent flow with suppressed momentum transfer in the sidewall (parallel to the magnetic field) boundary layers, a flow with laminar core and turbulent sidewall layers, a flow with laminar core and quasi-two-dimensional structures in the sidewall layers, and, at Ha=400, a completely laminarized flow.   

On the accurate simulation of magnetohydrodynamic turbulence and magnetic reconnection

The issue of adequate spatial resolution in numerical simulations of turbulence is studied in the context of decaying two-dimensional magnetohydrodynamics. By comparing simulations at varying resolution and at varying Reynolds numbers, the familiar criterion that the dissipation scale should be resolved is found to enable accurate computation of the spectrum, but fail for precise determination of higher-order statistical quantities. Examination of two straightforward diagnostics, the maximum of the kurtosis and the scale-dependent kurtosis, enables the development of simple tests for assessing adequacy of spatial resolution. The efficacy of the tests is confirmed by examining the distribution of magnetic reconnection rates in turbulence. Over-sampling the Kolmogorov dissipation scale by a factor of 3 allows accurate computation of the kurtosis, the scale-dependent kurtosis, and the reconnection rates. These tests may provide useful guidance for resolution requirements in many plasma computations involving turbulence and reconnection. [Phys. Plasmas 17, 082308 (2010)]   

Experimental investigation of free surface fluctuations and vortex dynamics in MHD flow

A magnetic field imposed on a conducting liquid can significantly alter the dynamics of large and small scale features within the flow. These effects may be critically important in turbulent heat transport for flowing liquid metal walls in a fusion reactor. Experiments have been conducted in the Liquid Metal Experiment (LMX) using a GaInSn eutectic alloy as a working fluid to investigate these effects. These experiments considered free-surface, wide aspect-ratio flow through a channel situated in a strong vertical magnetic field (up to $\textrm{Ha} \approx 50$, where $\textrm{Ha}$ is the ratio of electromagnetic to viscous forces). By tracking the deflection of the free surface in three locations, correlation analysis in both the down-stream and cross-stream directions gave insight into how the fluctuations were affected by the application of the magnetic field. Additionally, vorticies created in the wake of an obstruction responded dramatically to the applied field. Experimental results examining the damping of surface fluctuations and the characterization of vortices being shed from an obstruction will be presented.