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 magnetohydrodynamic (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. [1] and Xu et al. [2]. They differ from the simulations of Biferale et al. [3] due to differences of the ranges choosen for evaluating the structure functions. In Navier-Stokes turbulence intermittency is stronger than predicted by a multifractal approach of [3] whereas in MHD turbulence 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 PDFs works well for the Navier-Stokes case but in the MHD case just the tails are well described.Comment: to appear in J. Plasma Phy

Timescales of Turbulent Relative Dispersion

Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relativeComment: 4 pages, 3 figure

Lagrangian statistics in forced two-dimensional turbulence

We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is investigated. The results are compared to the three-dimensional case. In particular an analysis in terms of compensated cumulants reveals the transition from a strong non-Gaussian behavior with large tails to Gaussianity. The reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles.Comment: 8 figures, 1 tabl

Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the tail of the inter-tracer distance probability distribution. The tail approaches a pure exponential at large times, contradicting Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson's distribution.Comment: 21 page

Dispersion Relations for Thermally Excited Waves in Plasma Crystals

Thermally excited waves in a Plasma crystal were numerically simulated using a Box_Tree code. The code is a Barnes_Hut tree code proven effective in modeling systems composed of large numbers of particles. Interaction between individual particles was assumed to conform to a Yukawa potential. Particle charge, mass, density, Debye length and output data intervals are all adjustable parameters in the code. Employing a Fourier transform on the output data, dispersion relations for both longitudinal and transverse wave modes were determined. These were compared with the dispersion relations obtained from experiment as well as a theory based on a harmonic approximation to the potential. They were found to agree over a range of 0.9<k<5, where k is the shielding parameter, defined by the ratio between interparticle distance a and dust Debye length lD. This is an improvement over experimental data as current experiments can only verify the theory up to k = 1.5.Comment: 8 pages, Presented at COSPAR '0

Morphological adaptations of 3.22 Ga-old tufted microbial mats to Archean coastal habitats (Moodies Group, Barberton Greenstone Belt, South Africa)

Microbial life was well established and widespread by the Paleoarchean; however, the degree of evolutionary advancement such as microbial motility, intra- and inter-species interactions, phototropism, or oxygenic photosynthesis by that time remains highly debated. The 3.22 Ga Moodies Group in the Barberton Greenstone Belt (BGB, South Africa) are Earth's oldest well-preserved siliciclastic tidal deposits. They exhibit a unique assemblage of microbial mats, providing an excellent opportunity to decipher the morphological adaptations of microbial communities to different paleoenvironmental settings. The fossil mats are preserved as kerogenous laminations (0.5–1 mm thick) that can be traced laterally for ∼15 km in a ∼1000 m-thick succession of fine- to coarse-grained tidal sandstones and conglomerates. We here present a detailed stratigraphic and depositional facies analysis, documenting the association of the three principal mat morphotypes with specific environmental settings: (1) planar-type in coastal floodplain, (2) wavy-type in intertidal, and (3) tufted-type in upper inter- to supratidal facies. All mat types indicate a flourishing phototrophic biota; moreover, the tufted morphology suggests an intricate level of coordinated growth commonly known from cyanobacterial mats in modern environments

General properties and analytical approximations of photorefractive solitons

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and suggest various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r