Turbulent resistivity in wavy two-dimensional magnetohydrodynamic turbulence

2008 ◽  
Vol 595 ◽  
pp. 173-202 ◽  
Author(s):  
SHANE R. KEATING ◽  
P. H. DIAMOND
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Two Dimensions ◽  
Magnetic Potential ◽  
Turbulence Theory ◽  
Two Dimensional ◽  
Restoring Force ◽  
Constrained System ◽  
Magnetohydrodynamic Turbulence

The theory of turbulent resistivity in ‘wavy’ magnetohydrodynamic turbulence in two dimensions is presented. The goal is to explore the theory of quenching of turbulent resistivity in a regime for which the mean field theory can be rigorously constructed at large magnetic Reynolds number Rm. This is achieved by extending the simple two-dimensional problem to include body forces, such as buoyancy or the Coriolis force, which convert large-scale eddies into weakly interacting dispersive waves. The turbulence-driven spatial flux of magnetic potential is calculated to fourth order in wave slope – the same order to which one usually works in wave kinetics. However, spatial transport, rather than spectral transfer, is the object here. Remarkably, adding an additional restoring force to the already tightly constrained system of high Rm magnetohydrodynamic turbulence in two dimensions can actually increase the turbulent resistivity, by admitting a spatial flux of magnetic potential which is not quenched at large Rm, although it is restricted by the conditions of applicability of weak turbulence theory. The absence of Rm-dependent quenching in this wave-interaction-driven flux is a consequence of the presence of irreversibility due to resonant nonlinear three-wave interactions, which are independent of collisional resistivity. The broader implications of this result for the theory of mean field electrodynamics are discussed.

scholarly journals High harmonic generation in two-dimensional Mott insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher Orthodoxou ◽  
Amelle Zaïr ◽  
George H. Booth
Keyword(s):  
Quantum Monte Carlo ◽  
Strong Field ◽  
High Harmonic ◽  
Mean Field ◽  
Laser Pulses ◽  
Two Dimensions ◽  
Mott Insulators ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
Mean Field Model

AbstractWith a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high-frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.

scholarly journals Large-scale dynamo action of magnetized Taylor–Couette flows

2020 ◽  
Vol 493 (1) ◽  
pp. 1249-1260
Author(s):  
G Rüdiger ◽  
M Schultz
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Single Mode ◽  
Eddy Diffusivity ◽  
Magnetic Reynolds Number ◽  
Dynamo Model ◽  
Turbulence Energy ◽  
Dynamo Action ◽  
Taylor Couette

ABSTRACT A conducting Taylor–Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler–Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining α effect and eddy diffusivity. If both degenerated modes with m = ±1 are excited with the same power then the global α effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite α effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an α2 dynamo. Moreover, an αΩ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm ≃ 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, ηT ≃ η. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.

GRANULAR TURBULENCE IN TWO DIMENSIONS: MICROSCALE REYNOLDS NUMBER AND FINAL CONDENSED STATES

2012 ◽  
Vol 23 (04) ◽  
pp. 1250032 ◽  
Author(s):  
MASAHARU ISOBE
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Large Scale ◽  
Strong Relationship ◽  
Two Dimensions ◽  
Condensed State ◽  
Einstein Condensation ◽  
Two Dimensional ◽  
Developed Turbulence ◽  
Granular Gas

Granular gases from the viewpoint of "two-dimensional turbulence" are investigated. In the quasi-elastic and thermodynamic limit, we obtained clear evidence for an enstrophy (square of vorticity) cascade and -3 exponent in the Kraichnan–Leith–Bachelor energy spectrum by performing large-scale (N ~ 16.8 million number of disks) event-driven molecular dynamics simulations. In these calculations, the enstrophy dissipation rate showed a strong relationship with the evolution of the exponent in the energy spectrum. The growth of the Reynolds number based on the microscale confirmed that the enstrophy cascade regime was that of fully developed turbulence. Moreover, a condensed state resembling Bose–Einstein condensation in decaying two-dimensional Navier–Stokes turbulence also appeared as the final attractor of the evolving granular gas in the long time limit.

scholarly journals The effect of velocity shear on dynamo action due to rotating convection

2013 ◽  
Vol 717 ◽  
pp. 395-416 ◽  
Author(s):  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Velocity Shear ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Rotating Convection ◽  
The Magnetic Field

AbstractRecent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

scholarly journals Turbulence in Large-Scale Two-Dimensional Balanced Hard Sphere Gas Flow

Atmosphere ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1520
Author(s):  
Rafail V. Abramov
Keyword(s):  
Turbulent Flows ◽  
Hard Sphere ◽  
Large Scale ◽  
Gas Flow ◽  
Spatial Scales ◽  
Mean Field ◽  
Current Work ◽  
Two Dimensional ◽  
Dynamical Mechanism ◽  
Wide Range

In recent works, we developed a model of balanced gas flow, where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large-scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. However, the air density rapidly decays with altitude, roughly by an order of magnitude each 15–20 km. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large-scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.

scholarly journals Stationary states of two-dimensional magnetohydrodynamic turbulence: non-dissipative limit

1979 ◽  
Vol 22 (3) ◽  
pp. 385-396 ◽  
Author(s):  
Ronald Calinon ◽  
Danilo Merlini
Keyword(s):  
Gibbs Measure ◽  
Existence And Uniqueness ◽  
Canonical Ensemble ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Stationary States ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Magnetohydrodynamic Turbulence ◽  
Statistical Solutions

A class of exact stationary statistical states for the inviscid magnetohydrodynamic equations in two dimensions and in various geometries is found and the corresponding fluctuation spectra are calculated. Some solutions agree with previous computations in the canonical ensemble while other solutions are found. In particular, the Navier—Stokes limit is recovered and maximum cross helicity solutions exist in two dimensions. The difficulty of proving existence and uniqueness of statistical solutions for non-dissipative two-dimensional turbulence is quoted in terms of rugged constants and associated Gibbs measure.

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