Wolf-Christian Müller

Scaling properties of three-dimensional magnetohydrodynamic turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence with finite magnetic helicity are obtained from direct numerical simulations using 512(3) modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology. The scaling exponents of the structure functions can be described by a modified She-Leveque model zeta(p) = p/9+1-(1/3)(p/3), corresponding to basic Kolmogorov scaling and sheetlike dissipative structures. In particular, we find zeta(2) approximately 0.7, consistent with the energy spectrum E(k) approximately k(-5/3) as observed in the solar wind, and zeta(3) approximately 1, confirming a recent analytical result.

Spectral Energy Dynamics in Magnetohydrodynamic Turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024(3) collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E(R)k=|E(M)k - E(K)k|, and total energy, Ek=E(K)k+E(M)k, are observed to scale self-similarly in the inertial range as E(R)k approximately k(-7/3), E(k)approximately k(-5/3) (isotropic case) and E(R)(k(perpendicular) approximately k(-2)(perpendicular), E(k(perpendicular))approximately k(-3/2)(perpendicular) (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields E(R)k approximately kE2(k), which is confirmed by the simulations.

Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence

A comprehensive picture of three-dimensional (3D) isotropic magnetohydrodynamic (MHD) turbulence is presented based on the first 5123-mode numerical simulations performed. Both temporal and spatial scaling properties are studied. For finite magnetic helicity H the energy decay is governed by the constancy of H and the decrease of the ratio of kinetic and magnetic energy Γ=EK/EM. A simple model consistent with a series of simulation runs predicts the asymptotic decay laws E∼t−1/2, EK∼t−1. For nonhelical MHD turbulence, H≃0, the energy decays faster, E∼t−1. The energy spectrum follows a k−5/3 law, clearly steeper than k−3/2 previously found in 2D MHD turbulence. The scaling exponents of the structure functions are consistent with a modified She–Leveque model ζpMHD=p/9+1−(1/3)p/3, which corresponds to a basic Kolmogorov scaling and sheet-like dissipative structures. The difference between the 3D and the 2D behavior can be related to the eddy dynamics in 3D and 2D hydrodynamic turbulence.

Dynamics of the fusion process

Abstract The binary reaction products from the interaction of a 208Pb beam with targets of 26Mg, 27Al, 48Ca, 50Ti, 52Cr, 58Fe and 64Ni have been studied with the aid of a large position-sensitive ring counter, operated in a two-particle coincidence mode. The intensity of γ-rays and X-rays per event was also recorded. Within a broad range around mass symmetry, the center of mass angular distributions, γ-ray multiplicities, total kinetic energy distributions, and absolute mass yields have been determined as a function of the bombarding energy, ranging from 1.0 to 1.8 times the interaction barrier. When analysed on the basis of fusion models, the cross section for the mass equilibration reaction demonstrates that deformations induced at contact influence the fusion of these heavy systems significantly and characteristically. The γ-ray multiplicities appear to be strongly influenced by statistical angular momentum components that remain with the fragments after separation. Their magnitudes indicate that during the reaction, the collision complex becomes at least as compact as the liquid-drop saddle shape appropriate to a non-rotating nucleus with the same total mass and charge. Finally, some angular distributions show that the entire process of coalescence and reseparation can occur before the system has made one-half revolution; i.e. within a time of 5–10 × 10−21 s. No X-ray emission from the combined system 208Pb + 48Ca is observed.

Statistical anisotropy of magnetohydrodynamic turbulence.

Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with k(-3/2) inertial-range scaling of the perpendicular energy spectrum. An intermittency model based on the log-Poisson approach, zeta(p)=p/g(2)+1-(1/g)(p/g), is able to describe the observed structure function scalings.

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method and using little to no explicit artificial viscosity. Codes that fall short in one or more of these areas are still useful, but they must compensate for higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices about choosing optimal applications for their specific astrophysical problems.

Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence

The performance of different dynamic gradient-diffusion type subgrid models is evaluated in large-eddy simulations (LES) of magnetohydrodynamic (MHD) turbulence with a maximum of 643 collocation points. The reference data stems from high-resolution direct numerical simulations of decaying and forced MHD turbulence with up to 5123 spectral modes. Comparisons between LES’ and the grid filtered reference systems are carried out regarding the temporal evolution of the global quantities kinetic and magnetic energy, cross helicity, magnetic helicity, and the spectra of energy and energy flux. The influence of the subgrid models on the statistical properties of the simulated flows is also examined. Apart from unconditionally dissipative models, direct divergence modeling and the effects of additional explicit filtering in combination with a tensor-diffusivity term are considered. A new genuine MHD subgrid model, based on the cross-helicity invariant, is presented and observed to perform outstandingly well.

Decay laws for three-dimensional magnetohydrodynamic turbulence

Decay laws for three-dimensional magnetohydrodynamic turbulence are obtained from high-resolution numerical simulations using up to 512^3 modes....

Structure and decay of rotating homogeneous turbulence

Navier―Stokes turbulence subject to solid-body rotation is studied by high-resolution direct numerical simulations (DNS) of freely decaying and stationary flows. Setups characterized by different Rossby numbers are considered. In agreement with experimental results strong rotation is found to lead to anisotropy of the direct nonlinear energy flux, which is attenuated primarily in the direction of the rotation axis. In decaying turbulence the evolution of kinetic energy follows an approximate power law with a distinct dependence of the decay exponent on the rotation frequency. A simple phenomenological relation between exponent and rotation rate reproduces this observation. Stationary turbulence driven by large-scale forcing exhibits k ―2 ⊥ -scaling in the rotation-dominated inertial range of the one-dimensional energy spectrum taken perpendicularly to the rotation axis. The self-similar scaling is shown to be the cumulative result of individual spectral contributions which, for low rotation rate, display k ―3 ⊥ -scaling near the k ∥ = 0 plane. A phenomenology which incorporates the modification of the energy cascade by rotation is proposed. In the observed regime the nonlinear turbulent interactions are strongly influenced by rotation but not suppressed. Longitudinal two-point velocity structure functions taken perpendicularly to the axis of rotation indicate weak intermittency of the k ∥ = 0 (2D) component of the flow while the intermittent scaling of k ∥ ≠ 0 (3D) fluctuations is well captured by a modified She―Leveque intermittency model which yields the expression ζ p = p/6 + 2(1 — (2/3) p/2 ) for the structure function scaling exponents.