scholarly journals Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 46 ◽  
Author(s):  
Hideaki Miura
Keyword(s):  
Energy Transfer ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Fluid Dynamic ◽  
Skin Depth ◽  
Wave Number ◽  
Larmor Radius ◽  
Mhd Turbulence ◽  
High Wave Number ◽  
Extended Mhd

Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on differences of Hall and extended MHD turbulence from MHD turbulence at a fully relaxed state. Magnetic and kinetic energies, energy spectra, energy transfer, vorticity and current structures were studied. The Hall and gyro-viscous terms change the energy transfer in the equations of motions to be forward-transfer-dominant while the magnetic energy transfer remains backward-transfer-dominant. The gyro-viscosity works as a kind of hyper-diffusivity, attenuating the kinetic energy spectrum sharply at a high wave-number region. However, this term also induces high-vorticity events more frequently than MHD turbulence, making the turbulent field more intermittent. Vortices and currents were found to be transformed from sheet to tubular structures under the influences of the Hall and/or the gyro-viscous terms. These observations highlight features of fluid-dynamic aspect of turbulence in sub-ion-scales where turbulence is governed by the ion skin depth and ion Larmor radius.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Scale Adaptive Simulation of Flows Past an Airfoil After Stall

2012 ◽  
Author(s):  
Lei Du ◽  
Fangfei Ning
Keyword(s):  
Isotropic Turbulence ◽  
Wave Number ◽  
Test Case ◽  
Turbulent Structures ◽  
High Wave Number ◽  
Adaptive Simulation ◽  
Separation Flows ◽  
Sas Model ◽  
Stable Flow ◽  
Massive Separation

The Scale Adaptive Simulation (SAS) models can keep standard RANS capabilities in stable flow regions but resolve turbulent structures in unsteady regions of flow field like LES. This RANS/LES property of SAS model relies on the v. Karman length-scale as a scale determining variable, which allows the model to automatically adapt to the appropriate length-scales in the simulated flows. Although SAS is young and still in developing, it has been proved to be very suitable for the predictions of massive separation flows. In the current study, the SST-SAS model is implemented in an in-house CFD code. First, the test case of decaying homogenous isotropic turbulence is selected for calibrating a constant associated with high wave number damping. Then, the simulation of flow past NACA 0021 airfoil at 60° attack angle is carried out for the validation of this turbulence model in our code. After that, the numerical results of NACA 0021 airfoil at a range of attack angles after stall are also presented for the comprehensive understanding of the SAS model.

scholarly journals Third-order structure functions for isotropic turbulence with bidirectional energy transfer

2019 ◽  
Vol 877 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Energy Transfer ◽  
Isotropic Turbulence ◽  
Full Range ◽  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Stratified Turbulence ◽  
Mhd Turbulence ◽  
Third Order ◽  
Transfer Rates

We derive and test a new heuristic theory for third-order structure functions that resolves the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally, for example, in rotating stratified turbulence or magnetohydrodynamical (MHD) turbulence. The theory has three parameters – namely the upscale/downscale energy transfer rates and the forcing scale – and it includes the classic inertial-range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence.

scholarly journals Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence

2009 ◽  
Vol 76 (1) ◽  
pp. 117-128 ◽  
Author(s):  
CHRISTOPHER J. WAREING ◽  
RAINER HOLLERBACH
Keyword(s):  
Energy Transfer ◽  
Governing Equation ◽  
Magnetic Energy ◽  
Linear Time ◽  
Background Field ◽  
Three Dimensions ◽  
Spectral Energy ◽  
Field Energy ◽  
Mhd Turbulence ◽  
Direction Parallel

AbstractDecaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k−2 law with increasing RB, the ratio of the nonlinear to linear time scales in the governing equation, consistent with theoretical predictions. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer and recent studies of 2D EMHD turbulence. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. In another similarity to 2D EMHD turbulence, relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, cascades of energy in 3D EMHD turbulence are found to be suppressed in all directions under the influence of a uniform background field. Energy transfer is further reduced in the direction parallel to the field, displaying scale-dependent anisotropy. Finally, the governing equation is found to yield a weak inverse cascade, at least partially transferring magnetic energy from small to large scales.

scholarly journals Hamiltonian magnetic reconnection with parallel electron heat flux dynamics

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
D. Grasso ◽  
E. Tassi
Keyword(s):  
Heat Flux ◽  
Magnetic Reconnection ◽  
Magnetic Energy ◽  
Fluid Model ◽  
Temperature Fluctuations ◽  
Skin Depth ◽  
Density Fluctuations ◽  
Larmor Radius ◽  
Flux Dynamics ◽  
Isothermal Fluid

We analyse, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a non-canonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Larmor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system.

scholarly journals Interaction of Very Large Scale Motion of Coherent Structures with Sediment Particle Exposure

Water ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 248
Author(s):  
Sencer Yücesan ◽  
Daniel Wildt ◽  
Philipp Gmeiner ◽  
Johannes Schobesberger ◽  
Christoph Hauer ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Numerical Study ◽  
Local Maximum ◽  
Wave Number ◽  
Exposure Level ◽  
Sediment Particle ◽  
High Wave Number ◽  
Large Scale Motion ◽  
Scale Motion

A systematic variation of the exposure level of a spherical particle in an array of multiple spheres in a high Reynolds number turbulent open-channel flow regime was investigated while using the Large Eddy Simulation method. Our numerical study analysed hydrodynamic conditions of a sediment particle based on three different channel configurations, from full exposure to zero exposure level. Premultiplied spectrum analysis revealed that the effect of very-large-scale motion of coherent structures on the lift force on a fully exposed particle resulted in a bi-modal distribution with a weak low wave number and a local maximum of a high wave number. Lower exposure levels were found to exhibit a uni-modal distribution.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

RESEARCH OF EXTERNAL MASS TRANSFER PROCESSES FOR ADSORPTION FROM SOLUTIONS IN A APPARATUS WITH STIRRING

2021 ◽  
pp. 11-20
Author(s):  
V. Solovej ◽  
K. Gorbunov ◽  
V. Vereshchak ◽  
O. Gorbunova
Keyword(s):  
Mass Transfer ◽  
Energy Spectrum ◽  
Energy Dissipation ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Wave Number ◽  
Wave Form ◽  
Local Isotropy ◽  
Stirred Vessel ◽  
Almost All

A study has been mode of transport-controlled mass transfer-controlled to particles suspended in a stirred vessel. The motion of particle in a fluid was examined and a method of predicting relative velocities in terms of Kolmogoroff’s theory of local isotropic turbulence for mass transfer was outlined. To provide a more concrete visualization of complex wave form of turbulence, the concepts of eddies, of eddy velocity, scale (or wave number) and energy spectrum, have proved convenient. Large scale motions of scale contain almost all of the energy and they are directly responsible for energy diffusion throughout the stirring vessel by kinetic and pressure energies. However, almost no energy is dissipated by the large-scale energy-containing eddies. A scale of motion less than is responsible for convective energy transfer to even smaller eddy sires. At still smaller eddy scales, close to a characteristic microscale, both viscous energy dissipation and convection are the rule. The last range of eddies has been termed the universal equilibrium range. It has been further divided into a low eddy size region, the viscous dissipation subrange, and a larger eddy size region, the inertial convection subrange. Measurements of energy spectrum in mixing vessel are shown that there is a range, where the so called -(5/3) power law is effective. Accordingly, the theory of local isotropy of Kolmogoroff can be applied because existence of the internal subrange. As the integrated value of local energy dissipation rate agrees with the power per unit mass of liquid from the impeller, almost all energy from the impeller is viscous dissipated in eddies of microscale. The correlation for mass transfer to particles suspended in a stirred vessel is recommended. The results of experimental study are approximately 12 % above the predicted values.

scholarly journals Energy release and conversion by reconnection in the magnetotail

2005 ◽  
Vol 23 (10) ◽  
pp. 3365-3373 ◽  
Author(s):  
J. Birn ◽  
M. Hesse
Keyword(s):  
Energy Transfer ◽  
Energy Release ◽  
Large Scale ◽  
Magnetic Energy ◽  
Minor Role ◽  
Ohmic Dissipation ◽  
Particle Simulations ◽  
Minor Part ◽  
Reconnection Site ◽  
A Minor

Abstract. Magnetic reconnection is the crucial process in the release of magnetic energy previously stored in the magnetotail in association with substorms. However, energy transfer and dissipation in the vicinity of the reconnection site is only a minor part of the energy conversion. We discuss the energy release, transport, and conversion based on large-scale resistive MHD simulations of magnetotail dynamics and more localized full particle simulations of reconnection. We address in particular, where the energy is released, how it propagates and where and how it is converted from one form into another. We find that Joule (or ohmic) dissipation plays only a minor role in the overall energy transfer. Bulk kinetic energy, although locally significant in the outflow from the reconnection site, plays a more important role as mediator or catalyst in the transfer between magnetic and thermal energy. Generator regions with potential auroral consequences are located primarily off the equatorial plane in the boundary regions of the plasma sheet.

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