Superdiffusion in nearly stratified flows

In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in nearly stratified flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.     

Visualization of two-dimensional vortex flows in thin oscillating liquid films

A possibility of visualizing flows using random inhomogeneities of film thicknesses of different colors as particles for visualization is shown on an example of a vortex flow structure in an oscillating thin liquid film. Formation of vortex flows in a thin liquid film containing surface-active substances is investigated in experiments. The film is fixed horizontally along the edges of the cell vibrating in the vertical direction. Spatially homogeneous oscillations of the liquid film can excite different types of waves that generate two-dimensional vortex flows due to nonlinearity. We present results of experimental investigation of the structure of vortex flows in a thin film (0.5–10 μm) with rectangular boundaries. It has been revealed that, if the horizontal size of an inhomogeneous region is much smaller than the size of vortices, the inhomogeneities are transported by vortices and their interference pattern can be used for visualization of vortex flows.     

Formation and relaxation of two-dimensional vortex crystals in a magnetized pure-electron plasma

Systematic examinations are carried out experimentally about the contribution of background vorticity distributions (BGVD's) to the spontaneous formation and decay of ordered arrays (vortex crystals) composed of strong vortices (clumps) by using a pure-electron plasma. It is found that the BGVD level needs to be higher for an increasing number of clumps to form vortex crystals and that the number of the clumps constituting the crystal decreases in time as proportional to gamma lnt in contrast to proportional to t (-xi) with xi approximately 1 as accepted well in turbulence models. The decay rate gamma increases with the BGVD level. The observed configurations of the clumps cover the theoretically predicted catalogue of vortex arrays in superfluid helium, suggesting a possible relaxation path of the crystal states.     

Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma

Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser radiation pressure to yield a structure with liquid ordering. Analyzing the time series for mean-square displacement, superdiffusion is detected at a low but statistically significant level over a wide range of temperatures. The probability distribution function fits a Tsallis distribution, yielding q, a measure of nonextensivity for non-Gaussian statistics.     

Stationary vortical flows in two-dimensional plasma and in planetary atmospheres

We derive the equation governing the asymptotic stationary states generated by decaying turbulence in two-dimensional plasma and planetary atmosphere. These fluids may be described by the Charney-Hasegawa-Mima equation and their relaxation states show a high degree of organization in vortical flows, similar to the Euler fluid. We develop a field-theoretical framework and show that these systems attain at stationarity the extremum of an energy functional corresponding to self-dual fields.     

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.     

Heat transfer in a two-dimensional crystalline complex (dusty) plasma

Heating and heat transfer were studied in a two-dimensional crystalline complex plasma at the kinetic level. The lattice was formed of microspheres levitated in a plasma sheath. One half of the crystal was heated anisotropically to obtain higher kinetic temperatures in one direction and heat conduction was observed in real time. It was found that the longitudinal phonons conduct heat better than the transverse. The thermometric conductivity coefficient was measured to be 53 mm2/s for longitudinal heating and 30 mm2/s for transverse heating. Heat decay lengths and energy exchange times between the temperature components were determined.     

Fundamental and vortex solitons in a two-dimensional optical lattice

Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime the fundamental soliton is largely confined to one lattice site, whereas the vortex state comprises four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and the vortex solitons spread over many lattice sites. We further show that fundamental and the vortex solitons are stable against small perturbations in the strong localization regime.     

Ballooning vortex in a magnetized plasma

The existence of a ballooning solitary vortex in an inhomogeneous plasma immersed in crossed magnetic and gravitational fields is demonstrated.     

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L₂-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L₂-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.     

Tracking birth of vortex in flows

In order to avoid undesired effects from vortices in many industrial processes, it is important to know the set of operating parameters at which the flow does not have recirculation. The map of these conditions in the parameter space is called vortex-free operating window. Here, we propose an efficient way to construct such window automatically without expensively checking every possible flow states. The proposed technique is based on tracking a path in the parameter space at which the local kinematic condition at a stagnation point for vortex birth is satisfied. This multiparameter continuation is performed by solving an augmented Navier–Stokes system. In the augmented system, the birth condition and the governing equations was represented in Galerkin’s finite element context. We used the proposed method in two important coating flows with free surfaces: single-layer slot coating and forward roll coating.     

Wave-induced bed flows by a Lagrangian vortex scheme

Nominally 2-dimensional viscous flow induced by gravity waves over a spatially periodic bed is simulated by a Lagrangian vortex scheme. A vortex sheet is introduced on the surface at each time step to satisfy the zero velocity conditions. The sheet is discretised; the vortex-in-cell method is used to convect vorticity and random walks are added to effect viscous diffusion. Good agreement with analytical theory is obtained for velocity profiles in uniform sinusoidal flow and for mass transport due to linear waves. Mass transport for finite amplitude waves is also obtained. For separated flow over rippled beds, which is still liminar, a vortex decay factor is required to produce agreement with experiment and is thought to compensate for large scale 3-dimensional effects.     

Heat transport in a two-dimensional complex (dusty) plasma at melting conditions

The heat transport in a two-dimensional complex (dusty) plasma undergoing a phase transition was studied experimentally. A single layer of highly charged polymer microspheres was suspended in a plasma sheath. A part of this lattice was heated by two counterpropagating focused laser beams that moved rapidly around in the lattice and provided short intense random kicks to the particles. Above a threshold, the lattice locally melted. The spatial profiles of the particle kinetic temperature were analyzed to find a thermal conductivity, which did not depend on temperature.     

Dissipative longitudinal solitons in a two-dimensional strongly coupled complex (dusty) plasma

Solitary waves are experimentally studied in a monolayer hexagonal dust lattice which is formed from monodisperse plastic microspheres and levitated in the sheath of an rf discharge. It is found that the product of the soliton amplitude and the square of the soliton width is constant as the soliton propagates. The analytical theory describing the experiment is based on the equations of motion written for a linear chain. It takes into account damping, dispersion, and nonlinearity. The numerical simulation of a linear chain produces double solitons like those observed in the experiment.     

Electric field in two-dimensional complex plasma crystal:Simulated lattices

We focus on molecular dynamics simulated two-dimensional complex plasma crystals. We use rigid walls as a confinement force and produce square and rectangular crystals. We report various types of two-row crystals. The narrow and long crystals are likely to be used as wigglers; therefore, we simulate such crystals. Also, we analyze the electric fields of simulated crystals. A bit change in lattice parameters can change the internal structures of crystals and their electric fields notably. These parameters are the number of grains, grains charge, length, and width of the crystal. With the help of electric fields, we show the details of crystal structures.