Non-equilibrium temperatures in steady-state systems with conserved energy

We study a class of non-equilibrium lattice models describing local redistributions of a globally conserved quantity, which is interpreted as an energy. A particular subclass can be solved exactly, allowing to define a statistical temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. We compute the response function and find that when the fluctuation-dissipation relation is linear, the slope T_{FD}^{-1} of this relation differs from the inverse temperature T_{th}^{-1}. We argue that T_{th} is physically more relevant than T_{FD}, since in the steady-state regime, it takes equal values in two subsystems of a large isolated system. Finally, a numerical renormalization group procedure suggests that all models within the class behave similarly at a coarse-grained level, leading to a new parameter which describes the deviation from equilibrium. Quantitative predictions concerning this parameter are obtained within a mean-field framework.Comment: 16 pages, 2 figures, submitted to Phys. Rev.

Coriolis force in Geophysics: an elementary introduction and examples

We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that reason of pedagogical and practical interest. Our aim is to model them in a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic

Analysis of fast turbulent reconnection with self-consistent determination of turbulence timescale

We present results of Reynolds-averaged turbulence model simulation on the problem of magnetic reconnection. In the model, in addition to the mean density, momentum, magnetic field, and energy equations, the evolution equations of the turbulent cross-helicity $W$, turbulent energy $K$ and its dissipation rate $\varepsilon$ are simultaneously solved to calculate the rate of magnetic reconnection for a Harris-type current sheet. In contrast to previous works based on algebraic modeling, the turbulence timescale is self-determined by the nonlinear evolutions of $K$ and $\varepsilon$, their ratio being a timescale. We compare the reconnection rate produced by our mean-field model to the resistive non-turbulent MHD rate. To test whether different regimes of reconnection are produced, we vary the initial strength of turbulent energy and study the effect on the amount of magnetic flux reconnected in time.Comment: 10 pages, 7 figure

Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate $\gamma$ for the KHI decreases with increasing the width of velocity transition layer ${D_{v}}$ but increases with increasing the width of density transition layer ${D_{\rho}}$. After the initial transient period and before the vortex has been well formed, the linear growth rates, $\gamma_v$ and $\gamma_{\rho}$, vary with ${D_{v}}$ and ${D_{\rho}}$ approximately in the following way, $\ln\gamma_{v}=a-bD_{v}$ and $\gamma_{\rho}=c+e\ln D_{\rho} ({D_{\rho}}<{D_{\rho}^{E}})$, where $a$, $b$, $c$ and $e$ are fitting parameters and ${D_{\rho}^{E}}$ is the effective interaction width of density transition layer. When ${D_{\rho}}>{D_{\rho}^{E}}$ the linear growth rate $\gamma_{\rho}$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].Comment: Accepted for publication in PR

Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates

We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov $k^{-5/3}$ power law over almost a decade of length or wavenumber ($k$) scales. The kinetic energy spectrum of regime (C) exhibits a clear $k^{-3/2}$ power law associated with an inertial range for weak-wave turbulence, and a $k^{-7/2}$ power law for high wavenumbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.Comment: 11 pages, 10 figures. Minor updates to text and figures 1, 2 and

Large scale flow effects, energy transfer, and self-similarity on turbulence

The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256^3 to 1024^3, are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows

The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

(abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.Comment: 35 pages, 22 figures, revtex style, submitted to PR

A lattice Boltzmann study of non-hydrodynamic effects in shell models of turbulence

A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same time scale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer time scale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non hydrodynamic fields.Comment: 17 pages, 3 figures, submitted to Physica