柱几何Rayleigh-Taylor不稳定性的数值模拟

给出了柱几何中流体力学方程组及其在数值模拟中采用的计算方法。对二维柱几何Rayleigh-Taylor不稳定性进行数值模拟,在线性阶段与线性理论符合得很好;不稳定性增长进入非线性区域的阈值依赖于界面的位置,并且明显不同于平面情况。     

Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence

Clustering (or preferential concentration) of inertial particles suspended in a homogeneous, isotropic turbulent flow is strongly influenced by the smallest scales of the turbulence. In particle-laden large-eddy simulations (LES) of turbulence, these small scales are not captured by the grid and hence their effect on particle motion needs to be modelled. In this paper, we use a subgrid model based on kinematic simulations of turbulence (Kinematic Simulation based SubGrid Model or KSSGM), for the first time in the context of predicting the clustering and the relative velocity statistics of inertial particles. This initial study focuses on the special case of inertial particles in the absence of gravitational settling. We show that the KSSGM gives excellent predictions for clustering in a priori tests for inertial particles with St ≥ 2.0, where St is the Stokes number, defined as the ratio of the particle response time to the Kolmogorov time-scale. To the best of our knowledge, the KSSGM represents the first model that has been shown to capture the effect of the subgrid scales on inertial particle clustering for St ≥ 2.0. We also show that the mean inward radial relative velocity between inertial particles (?w_r?^(?), which enters into the formula for the collision kernel) is accurately predicted by the KSSGM for all St. We explain why the model captures clustering at higher St?but not for lower St?, and provide new insights into the key statistical parameters of turbulence that a subgrid model would have to describe, in order to accurately predict clustering of low-St?particles in an LES.     

Dynamic simulations of the dipolar driven demagnetization process of magnetic multi-core nanoparticles

In this work, we investigate dynamically the dipolar driven demagnetization process of magnetic multi-core particles by solving the Landau-Lifshitz equation for single-domain particles distributed on a three-dimensional sphere. We analyze the relaxation time in respect to different geometry and material parameters. Further we show that the demagnetization times differ from the behaviour of a single magnetic sphere in the case of low damping. To explain these dynamics nanoparticular systems of different dimensions are investigated. We show that deviations can be attributed to a confinement of the relaxation dynamics to a lower dimensional submanifold of the k-space.     

An alternative approach to field-aligned coordinates for plasma turbulence simulations

In this work, a new approach to field-aligned coordinates for plasma turbulence is presented, in which the position along the field lines is identified by the toroidal angle. The several advantages of the new approach are discussed. It is also shown that the approach can be generalised to get rid of magnetic coordinates in the poloidal plane altogether. Tests are carried out by comparing codes implementing a basic ion temperature gradient turbulence model with the old and the new methods. Results show an unexpected property of the model, that localized large parallel gradients can intermittently appear in the turbulent regime.     

Cyclokinetic models and simulations for high-frequency turbulence in fusion plasmas

Gyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlinearly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency (ion cyclotron frequency) regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1.This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22(5), 056101 (2015)] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian (or continuum) scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 (2015)]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy.By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω* values with stable ion cyclotron modes. The gyrokinetic approximation is found to break down when the density perturbation exceeds 20%, or when the ratio of nonlinear E×B frequency over ion cyclotron frequency exceeds 20%. This result indicates that the density perturbation of the Tokamak L-mode near-edge is not sufficiently large for breaking the gyro-phase averaging. For cyclokinetic simulations with sufficiently unstable ion cyclotron (IC) modes and sufficiently low Ω* ～10, the high-frequency component of the cyclokinetic transport can exceed that of the gyrokinetic transport. However, the low-frequency component of the cyclokinetic transport does not exceed that of the gyrokinetic transport. For higher and more physically relevant Ω* ?50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport remains smaller than that of the gyrokinetic transport. In conclusion, the “L-mode near-edge short-fall” phenomenon, observed in some low-frequency gyrokinetic turbulence transport simulations, does not arise owing to the nonlinear coupling of high-frequency ion cyclotron motion to low-frequency drift motion.     

Monte Carlo simulations of a tethered membrane model on a disk with intrinsic curvature

A first-order phase transition separating the smooth phase from the crumpled one is found in a fixed connectivity surface model defined on a disk. The Hamiltonian contains the Gaussian term and an intrinsic curvature term.     

A scalar model for MHD turbulence

A model for homogeneous MHD turbulence is proposed. Nonlinear interactions acts between nearest neighbours in a discretized wavenumbers space and conservation properties (total energy and v-b correlation) are verified. The model can be truncated at will. With three modes, a bifurcation analysis is given. In the turbulent case (dissipation and kinetic forcing are present) one obtains time fluctuations at all scales and time-averaged power law spectra, the small scales exhibit intermittency effects. Typical MHD phenomena such as the dynamo effect or the increase of v-b correlation in the decaying cases are also observed.     

Differential model for 2D turbulence

We present a phenomenological model for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order differential equation. This equation respects the scaling properties of the original Navier-Stokes equations, and it has both the −5/3 inverse-cascade and the −3 direct-cascade spectra. In addition, our model has Raleigh-Jeans thermodynamic distributions as exact steady state solutions. We use the model to derive a relation between the direct-cascade and the inverse-cascade Kolmogorov constants, which is in good qualitative agreement with the laboratory and numerical experiments. We discuss a steady state solution where both the enstrophy and the energy cascades are present simultaneously, and we discuss it in the context of the Nastrom-Gage spectrum observed in atmospheric turbulence. We also consider the effect of the bottom friction on the cascade solutions and show that it leads to an additional decrease and finite-wavenumber cutoffs of the respective cascade spectra, which agrees with the existing experimental and numerical results. The text was submitted by the authors in English.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

Instabilities responsible for magnetic turbulence in laboratory rotating plasma

Instabilities responsible for magnetic turbulence in laboratory rotating plasma are investigated. It is shown that the plasma compressibility gives a new driving mechanism in addition to the known Velikhov effect due to the negative rotation frequency gradient. This new mechanism is related to the perpendicular plasma pressure gradient, while the density gradient gives an additional drive depending also on the pressure gradient. It is shown that these new effects can manifest themselves even in the absence of the equilibrium magnetic field, which corresponds to nonmagnetic instabilities.     

Adaptation of mesoscale turbulence parameterisation schemes as RANS closures for ABL simulations

The present study presents different k-ε turbulence closures for atmospheric boundary layer flows using computational fluid dynamics (CFD) simulations that are consistent with inflow conditions from numerical weather prediction (NWP) simulations. Eight different mesoscale turbulence parameterisation schemes of the Weather Research and Forecasting (WRF) model are covered. To ensure consistency between the NWP and CFD simulations, different closure coefficients of the k ? ε turbulence model for each NWP scheme are proposed. This is achieved by combining production–dissipation closure coefficient relationships based on the Monin–Obukhov similarity theory and the formulation based on the Coriolis parameter proposed by Detering and Etling. The proposed methodology has been implemented in the open source CFD toolbox OpenFOAM and is demonstrated at near-neutral stability conditions for the classical Askervein Hill case.     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

Electrical turbulence as a result of the critical curvature for propagation in cardiac tissue

In cardiac tissue, the propagation of electrical excitation waves is dependent on the active properties of the cell membrane (ionic channels) and the passive electrical properties of cardiac tissue (passive membrane properties, distribution of gap junctions, and cell shapes). Initiation of cardiac arrhythmias is usually associated with heterogeneities in the active and/or passive properties of cardiac tissue. However, as a result of the effect of wave front geometry (curvature) on propagation of cardiac waves, inexcitable anatomical obstacles, like veins and arteries, may cause the formation of self-sustained vortices and uncontrolled high-frequency excitation in normal homogeneous myocardium. (c) 1998 American Institute of Physics.