Rainer Grauer

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.

Adaptive Mesh Refinement for Singular Current Sheets in Incompressible Magnetohydrodynamic Flows

The formation of current sheets in ideal incompressible magnetohydrodynamic flows in two dimensions is studied numerically using the technique of adaptive mesh refinement. The growth of current density is in agreement with simple scaling assumptions. As expected, adaptive mesh refinement shows to be very efficient for studying singular structures compared to nonadaptive treatments.

Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented numerical schemes include standard finite-differences as well as shock-capturing central schemes, both in connection with Runge-Kutta type integrators. Parallel execution is achieved through a configurable hybrid of POSIX-multi-threading and MPI distribution with dynamic load balancing. One-, two- and three-dimensional test computations for the Euler equations have been carried out and show good parallel scaling behavior. The Racoon framework is currently used to study the formation of singularities in plasmas and fluids.

Scaling of high-order structure functions in magnetohydrodynamic turbulence

A phenomenological model for the description of intermittency corrections in magnetohydrodynamic flows is presented. The strength of the model lies in its lack of adjustable parameters. A comparison to measurements in the solar wind is presented.

Numerical simulations of possible finite time singularities in the incompressible Euler equations : Comparison of numerical methods

Abstract The numerical simulation of the 3D incompressible Euler equations is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods. Based on this comparison, a Kida–Pelz-like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given. This estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective.

Kinetic Vlasov simulations of collisionless magnetic reconnection

A fully kinetic Vlasov simulation of the Geospace Environment Modeling Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions fk (k=i,e) are discretized on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm’s law are compared by calculating each of the terms from the moments of the fk. The important role of the off-diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X line is found to be dominated by the nongyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic...

Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields

The standard approach for integrating the multidimensional Vlasov equation using grid based, conservative schemes is based on a time splitting approach. Here, we show that although the truncation error is of second order, time splitting can introduce systematic heating of the plasma. We introduce a backsubstitution method, which not only avoids this deficiency but also is computationally less expensive. The general approach is demonstrated in conjunction with Boris’ scheme for evaluating the characteristics.

Local turbulence simulations for the multiphase ISM

In this paper, we show results of numerical simulations for the turbulence in the interstellar medium (ISM). These results were obtained using a Riemann solver-free numerical scheme for high-Mach number hyperbolic equations. Here, we especially concentrate on the physical properties of the ISM. That is, we do not present turbulence simulations trimmed to be applicable to the ISM. The simulations are rather based on physical estimates for the relevant parameters of the interstellar gas. Applying our code to simulate the turbulent plasma motion within a typical interstellar molecular cloud, we investigate the influence of different equations of state (isothermal and adiabatic) on the statistical properties of the resulting turbulent structures. We find slightly different density power spectra and dispersion maps, while both cases yield qualitatively similar dissipative structures, and exhibit a departure from the classical Kolmogorov case towards a scaling described by the She-Leveque model. Solving the full energy equation with realistic heating/cooling terms appropriate for the diffuse interstellar gas (DIG), we are able to reproduce a realistic two-phase distribution of cold and warm plasma. When extracting maps of polarized intensity from our simulation data, we find encouraging similarity to actual observations. Finally, we compare the actual magnetic field strength of our simulations to its value inferred from the rotation measure. We find these to be systematically different by a factor of about 1.15, thus highlighting the often-underestimated influence of varying line-of-sight particle densities on the magnetic field strength derived from observed rotation measures.

Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magneto- hydrodynamic (MHD) flows. Numerical simulations were performed with up to 1024 3 collocation points and 10 million particles in the Navier-Stokes case and 512 3 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. (2004 New J. Phys. 6, 116) and Xu et al. (2006 Phys. Rev. Lett.96, 024503). They differ from the simulations of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) due to differences of the ranges chosen for evaluating the structure functions. In Navier- Stokes turbulence intermittency is stronger than predicted by the multifractal approach of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) whereas in MHD tur- bulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration probability density functions works well for the Navier-Stokes case but in the MHD case just the tails are well described.

Darwin-Vlasov simulations of magnetised plasmas

We present a new Vlasov code for collisionless plasmas in the nonrelativistic regime. A Darwin approximation is used for suppressing electromagnetic vacuum modes. The spatial integration is based on an extension of the flux-conservative scheme, introduced by Filbet et al. [F. Filbet, E. Sonnendrucker, P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (2001) 166]. Performance and accuracy is demonstrated by comparing it to a standard finite differences scheme for two test cases, including a Harris sheet magnetic reconnection scenario. This comparison suggests that the presented scheme is a promising alternative to finite difference schemes.