Statistical properties of an ensemble of vortices interacting with a turbulent field

We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by path-integral methods. The function space is the statistical ensemble composed of two parts, the first one representing the vortices influenced by the turbulence and the second one the turbulent field scattered by the randomly placed vortices.Comment: Third version; Important corrections in the normalization for the gas of vortices, et

Diffusion and dispersion of passive tracers: Navier-Stokes versus MHD turbulence

A comparison of turbulent diffusion and pair-dispersion in homogeneous, macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic (MHD) turbulence based on high-resolution direct numerical simulations is presented. Significant differences between MHD and NS systems are observed in the pair-dispersion properties, in particular a strong reduction of the separation velocity in MHD turbulence as compared to the NS case. It is shown that in MHD turbulence the average pair-dispersion is slowed down for $\tau_\mathrm{d}\lesssim t\lesssim 10 \tau_\mathrm{d}$, $\tau_\mathrm{d}$ being the Kolmogorov time, due to the alignment of the relative Lagrangian tracer velocity with the local magnetic field. Significant differences in turbulent single-particle diffusion in NS and MHD turbulence are not detected. The fluid particle trajectories in the vicinity of the smallest dissipative structures are found to be characterisically different although these comparably rare events have a negligible influence on the statistics investigated in this work.Comment: Europhysics Letters, in prin

Thermal conduction and particle transport in strong MHD turbulence, with application to galaxy-cluster plasmas

We investigate field-line separation in strong MHD turbulence analytically and with direct numerical simulations. We find that in the static-magnetic-field approximation the thermal conductivity in galaxy clusters is reduced by a factor of about 5-10 relative to the Spitzer thermal conductivity of a non-magnetized plasma. We also estimate how the thermal conductivity would be affected by efficient turbulent resistivity.Comment: Major revision: higher resolution simulations lead to significantly different conclusions. 26 pages, 10 figure

Renormalized dissipation in the nonconservatively forced Burgers equation

A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given

Hamiltonian description of convective-cell generation

The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted

Influence of zonal flows on unstable drift modes in ETG turbulence

The linear instability of the electron temperature gradient (ETG) driven modes in the presence of zonal flows is investigated. Random and deterministic $cos$ - like profiles of the zonal flow are considered. It is shown that the presence of shearing by zonal flows can stabilize the linear instability of ETG drift modes

Trajectory structures and transport

The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.Comment: Latex file 19 pages, includes 12 EPS figures. Extended version of the invited talk at the ITCPP, Santorini, 200

Hamiltonian Description of Convective-cell Generation

The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted