Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma = 6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at freestream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibility effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely tO OCCUr.     

Derivation of a Nonlinear Reynolds Stress Model Using Renormalization Group Analysis and Two-Scale Expansion Technique

Adopting Yoshizawa＇s two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.     

Supersonic Turbulent Boundary Layer： DNS and RANS

We assess the performance of a few turbulence models for Reynolds averaged Navier-Stokes （RANS） simulation of supersonic boundary layers, compared to the direct numerical simulations （DNS） of supersonic flat-plate turbulent boundary layers, carried out by Gao et al. [Chin. Phys. Lett. 22（2005）1709] and Huang et al. [Sci. Chin. 48 （2005） 614], as well as some available experimental data. The assessment is made for two test cases, with incoming Mach numbers and Reynolds numbers M = 2.25, Re = 365, 000//in, and M = 4.5, Re = 1.7 × 10^7/m, respectively. It is found that in the first case the prediction of RANS models agrees well with the DNS and the experimental data, while for the second case the agreement of the DNS models with experiment is less satisfactory. The compressibility effect on the RANS models is discussed.     

Activation of Hydrogen-Passivated Mg in GaN-Based Light Emitting Diode Annealing with Minority-Carrier Injection

We discuss an issue on the activation of p-GaN material under different annealing conditions and study the mechanism for the p-GaN activation. Under annealing in nitrogen, it is found that hydrogen cannot be completely removed from p-GaN. The experiments also indicate that rudimental hydrogen can exist stably in a certain state where hydrogen does not passivate the Mg acceptor in the sample annealing under bias. However, making additional annealing in nitrogen, we find that the steady state hydrogen can be decomposed and the Mg-H complex could generate again. Hydrogen remaining in the layer seems to play a major role in this reversible phenomenon.     

PIV Measurements and Mechanisms of Adjacent Synthetic Jets Interactions

Interactions of adjacent synthetic jet actuators with varying relative amplitude and the relative phase of driving voltage are measured using a particle image velocimetry （PIV）. Varying relative amplitude or relative phase of driving voltage of the adjacent actuators vectors the direction of the ensuing merged jet of the adjacent synthetic jets. The vectoring mechanism of the adjacent vortex pairs, attract-impact causing deflection （AICD）, is provided to explain why the merged jet is generally vectored to the side of the phase-leading synthetic jet or the synthetic jet with higher driving voltage.     

Effects of Different Plasma Energy Treatments on n-Type Al0.4Ga0.6N Material

El3ctronic properties, surface chemistry and surface morphology of plasma-treated n-Al0.4Ga0.6N material are studied by electrical contact measurements, atomic force microscopy and x-ray photoemission spectroscopy. Although excessive etching can cause the surface roughness to significantly increase, the nitrogen vacancies VN produced by the excessive etching can be compensated for by the negative effects of the rougher surface. Thus, VN produced by excessive etching plays a key role in Ohmic contact of high-A1 content AIGaN and it can reduce Ohmic contact resistance. The effect of rapid thermal annealing on the performance of n-Al0.4Ga0.6N can significantly reduce the etching damage caused by excessive etching.     

On the lower bound of net driving power in controlled duct flows

We examine mathematically the lower bound of the net driving power (i.e., the summation of pumping and actuation powers) of a controlled duct flow under a constant flow rate. The net power in a duct with arbitrary cross-section in the presence of the inertial term, blowing/suction from the wall, and arbitrary body forces can be decomposed into four terms: (1) dissipation due to the velocity profile of the Stokes flow (in other words, pumping power for the Stokes flow); (2) dissipation due to deviation of the mean velocity from the Stokes flow profile; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of the Stokes flow and the time-averaged blowing/suction velocity. Of these, the first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane channels. Namely, in such cases, the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.     

Fluid dynamical enstrophy and the number of optical vortices in a paraxial beam

Vortex-bearing optical beams have a tendency to maintain the maximum number of vortices during propagation. This tendency is reminiscent of the concept of enstrophy, which is a conserved quantity in two-dimensional fluid dynamics, and which is given in terms of the vorticity in the fluid. We derive the optical equivalent for the fluid vorticity and show that it represents the optical topological charge density in paraxial beams. It then follows that the optical equivalent of the enstrophy represents the total number of optical vortices on a cross-section of the beam. We then argue that this concept forms an important part of the tendency of paraxial beams to maintain their maximum number of vortices. As part of the derivation we provide a summary of some of the pertinent topological properties of phase functions.     

Persistency of material element deformation in isotropic flows and growth rate of lines and surfaces

We explore the consequence of isotropy on the growth of material lines and surfaces in complex flows. We show that the key parameter is the persistency , defined as the product of a typical stretching rate to its associated coherence time . In particular, we derive the dependence of the net growth rate of both lines and surfaces on . Their growth rates increase strongly with increasing persistencies for small , and then saturate for . Making use of measurements of Girimaji and Pope [1], we estimate the persistency to be of order 1 in isotropic turbulence. We then comment on the evolution of the shape of an initially spherical material blob. While its length increases, one of its tranverse dimension increases slowly and the other one decreases. This quasi-two-dimensional deformation leads a final ribbon-shape. Received 10 November 1999 and Received in final form 14 August 2000     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Observation of optical properties related to room-temperature ferromagnetism in co-sputtered Zn1−xCoxO thin films

We report on the analysis of optical transmittance spectra and the resulting ferromagnetic characteristics of sputtered Zn_1−xCo_xO films. Zn_1−xCo_xO films were prepared on (0001)-oriented Al₂O₃ substrates by the radio-frequency (rf) magnetron co-sputtering method. The XRD results showed that the crystallinity of films was properly maintained up to x=0.30 and no second phase peaks were detected up to x=0.40. The transmittance spectra showed both the increase of the absorption band intensity and the red shift of the absorption peak as well as the band edge with increasing x. We have proved experimentally that these changes depend on Co concentration. These optical properties suggest that sp-d exchange interactions and typical d-d transitions become activated with increasing x, which leads to the enhancement of ferromagnetic properties in Zn_1−xCo_xO films as shown in the AGM results. Therefore, it is concluded that the ferromagnetism derives from the substitution of Co²⁺ for Zn²⁺ without changing the wurtzite structure.     

Standing and travelling waves in the shallow-water circular hydraulic jump

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.     

Preparation and magnetoresistance of thin CrO2 films

Highly textured chromium dioxide (CrO₂) films have been deposited on Al₂O₃ single-crystal substrates by atmospheric pressure chemical vapor deposition method (CVD). X-ray diffraction patterns show that the CrO₂ films are (1 0 0)-oriented on Al₂O₃ (0 0 1) substrates, and are (1 0 1)-oriented on Al₂O₃ (0 1 2) substrates. Scanning electron microscopy images indicate that the (1 0 0)-oriented CrO₂ films grown on Al₂O₃ (0 0 1) substrates have smoother surface and better qualities than that grown on Al₂O₃ (0 1 2) substrate. At room temperature, the magnetoresistance of the (1 0 0)- and (1 0 1)-oriented CrO₂ films are nearly same, and both show a linear dependence on applied magnetic field. While at 80 K, the (1 0 1)-oriented CrO₂ films show a much larger magnetoresistance compared with the (1 0 0)-oriented CrO₂ films. The reasons are briefly discussed.     

Knotlike vortex lines in spinor BEC

In this paper the knotlike vortex lines in spinor Bose-Einstein condensates are studied. First it is shown that there are vortex line structures existing in spinor BEC, then we emphasize on the knotlike configurations and study the Faddeev-Niemi (F-N) model to discuss the topology of knots. The important meaning of F-N knot quantum number has been revealed: this number is just the total sum of all the self-linking and linking numbers of the knots family, and it is preserved in the splitting, the mergence and the intersection processes of knotlike vortex lines in spinor BEC.     

Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(ε³), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy. Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp     

A shell-model approach to fractal-induced turbulence

We present a shell-model of fractal induced turbulence which predicts that structure function scaling exponents decrease in absolute value as the fractal dimension of the turbulence-inducing fractal object increases. This qualitative prediction is in agreement with laboratory measurements. Finer details of the fractal induced turbulence statistics and dynamics depend on the fractal force's phases, i.e. on the detailed construction of the fractal stirrer. In a case of deterministic forcing phases, a critical fractal dimension exists below which the average rate of inter-scale energy transfer <T _n> is a decreasing function of the wavenumber k_n and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, <T _n> is an increasing function of k_n and the structure function scaling exponents deviate significantly from Kolmogorov values. Received 25 June 2001 / Received in final form 5 April 2002 Published online 19 July 2002     

Axisymmetric form of Kármán-Howarth equation and its limiting forms

Kinematics and dynamics of homogeneous axisymmetric turbulence have been derived with the assumption that the properties of the turbulence are invariant with respect to rotation about a preferred direction . In particular, the “axisymmetric" equivalent of Karman-Howarth “isotropic" equation is derived using Lindborg's representation of the two-point correlation tensors of homogeneous axisymmetric turbulence. When the more constraining assumption of isotropy is made, this equation reduces to the well-known Karman-Howarth equation. There are two interesting limiting forms of the axisymmetric Karman-Howarth equation: the axisymmetric form of the energy balance equation and the axisymmetric form of the vorticity balance equation. Received 1 July 1999 and Received in final form 9 November 1999     

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma = 0.7

Direct numerical simulation （DNS） of a spatially evolving fiat-plate boundary layer transition process at free stream Mach number 0. 7 is performed. Tollmien-Schlichting （T-S） waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the trallsition process plays an important role in the laminar breakdown process.     

Modification of alumina barrier-layer through re-anodization in an oxalic acid solution with fluoride additives

A new simple method for modification of the porous alumina barrier-layer is described and characterized by the voltammetric, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and electrochemical impedance spectroscopy (EIS) techniques. The method is based on re-anodization of porous alumina under galvanostatic conditions in the anodizing bath that, in addition to conventional anodization solution components, contains fluoride salts: (NH₄)₂SiF₆ or NH₄F. During first few minutes of alumina re-anodization, the sharp drop of anodizing voltage was observed, which is indicative of chemical/electrochemical transformations of the alumina barrier-layer. As a result, the scalloped structure of the barrier-layer changes drastically, becoming smooth and finely grained. Upon re-anodization, a significant loss of insulating ability of the barrier-layer and considerable increase in its capacitance were observed, while the variation of the constant phase element was found to be consistent with the oxide film morphology transformations observed by microscopy techniques. All these changes intensify with fluoride concentration increase. Curiously, (NH₄)₂SiF₆ exhibited about three-fold stronger effect on the barrier-layer properties than NH₄F, thus allowing us to hypothesize about possible chemical break up of SiF₆²⁻ anion and the formation of the AlF₃ phase inside the alumina pores.