Towards optimal explicit time-stepping schemes for the gyrokinetic equations

The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes measures to improve the efficiency of such computations, thereby making them more realistic. Explicit Runge-Kutta schemes are considered to be well suited for time-stepping. Although the numerical algorithms are often highly optimized, performance can still be improved by a suitable choice of the time-stepping scheme, based on spectral analysis of the underlying operator. Here, an operator splitting technique is introduced to combine first-order Runge-Kutta-Chebychev schemes for the collision term with fourth-order schemes for the remaining terms. In the nonlinear regime, based on the observation of eigenvalue shifts due to the (generalized) $E\times B$ advection term, an accurate and robust estimate for the nonlinear timestep is developed. The presented techniques can reduce simulation times by factors of up to three in realistic cases. This substantial speedup encourages the use of similar timestep optimized explicit schemes not only for the gyrokinetic equation, but also for other applications with comparable properties.Comment: 11 pages, 5 figures, accepted for publication in Computer Physics Communication

Contemporary soaring nomenclature

Considerable technical progress took place during the past two decades in the field of soaring. In contrast, basic terminology in many languages is lagging seriously. English, one of the leading languages, is no exception. Because of this situation, misunderstandings occur which under some circumstances may result in undesirable consequences, hindering further technical developments as well as soaring activities. Definitions were established and compiled by mid-1973, followed by minor additions (1974 and 1977)

Lagrangian Particle Statistics in Turbulent Flows from a Simple Vortex Model

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically

Anomalous Diffusion of particles with inertia in external potentials

Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a harmonic potential and a velocity-dependend damping are incorporated. Exact relations for moments for these cases are presented and the asymptotic behaviour for long times is discussed. Interestingly the bounding potential and the additional damping by itself lead to a subdiffussive behaviour, while acting together the particle becomes localized for long times.Comment: 12 pages, 8 figure

Identification of vortexes obstructing the dynamo mechanism in laboratory experiments

The magnetohydrodynamic dynamo effect explains the generation of self-sustained magnetic fields in electrically conducting flows, especially in geo- and astrophysical environments. Yet the details of this mechanism are still unknown, e.g., how and to which extent the geometry, the fluid topology, the forcing mechanism and the turbulence can have a negative effect on this process. We report on numerical simulations carried out in spherical geometry, analyzing the predicted velocity flow with the so-called Singular Value Decomposition, a powerful technique that allows us to precisely identify vortexes in the flow which would be difficult to characterize with conventional spectral methods. We then quantify the contribution of these vortexes to the growth rate of the magnetic energy in the system. We identify an axisymmetric vortex, whose rotational direction changes periodically in time, and whose dynamics are decoupled from those of the large scale background flow, is detrimental for the dynamo effect. A comparison with experiments is carried out, showing that similar dynamics were observed in cylindrical geometry. These previously unexpected eddies, which impede the dynamo effect, offer an explanation for the experimental difficulties in attaining a dynamo in spherical geometry.Comment: 25 pages, 12 figures, submitted to Physics of Fluid