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ABSTRACT: A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three
helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity
as well as for the magnetic field. The advantage of the method is the automatic conservation of all the ideal quadratic MHD
invariants. The number of coupling constants is however larger than in traditional shell models. This difficulty is worked
around by introducing an averaging procedure that allows to derive the shell model coupling constants directly from the MHD
equations. The resulting shell model is used to explore the influence of a helical forcing on the global properties of MHD
turbulence close to the onset of the dynamo regime.
Theoretical and Computational Fluid Dynamics 04/2012; 23(6):439-450. · 1.03 Impact Factor
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ABSTRACT: In previous work [1], an investigation of Kolmogorov flow for incompressible magnetohydrodynamics (MHD) was performed. It consists of a three-dimensional periodic flow driven by a unidirectional forcing varying on a transverse direction. In practice, the forcing is chosen to be fx = A sin(kfy), and fy = fz = 0. It was found that vorticity structures with long lifetimes can be formed in the turbulent regime. The presence of such structures may affect the transport of particles interacting with the flow as shown in this preliminary study.
Journal of Physics Conference Series 12/2011; 333(1):012010.
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ABSTRACT: Using a helical shell model of turbulence, Chen et al. (2003) showed that both helicity and energy dissipate at the Kolmogorov scale, independently from any helicity input. This is in contradiction with a previous paper by Ditlevsen & Giuliani (2001) in which, using a GOY shell model of turbulence, they found that helicity dissipates at a scale larger than the Kolmogorov scale, and does depend on the helicity input. In a recent paper by Lessinnes et al. (2011), we showed that this discrepancy is due to the fact that in the GOY shell model only one helical mode (+ or −) is present at each scale instead of both modes in the helical shell model. Then, using the GOY model, the near cancellation of the helicity flux between the + and − modes cannot occur at small scales, as it should be in true turbulence. We review the main results with a focus on the numerical procedure needed to obtain accurate statistics.
Journal of Physics Conference Series 12/2011; 318(4):042013.
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ABSTRACT: Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers.
11/2011;
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ABSTRACT: Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Physics of Plasmas 09/2011; 18(9):092303-092303-7. · 2.15 Impact Factor
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ABSTRACT: The scale locality of energy fluxes for magnetohydrodynamics (MHD) is
investigated numerically for stationary states of turbulence. Two types of
forces are used to drive turbulence, a kinetic force that acts only on the
velocity field and a kinetic-inductive forcing mechanism, which acts on the
velocity and magnetic fields alike. The analysis is performed in spectral
space, which is decomposed into a series of shells following a power law for
the boundaries. The triadic transfers occurring among these shells are computed
and the fluxes and locality functions are recovered by partial summation over
the relevant shells. Employing Kraichnan locality functions, values of 1/3 and
2/3 for the scaling exponents of the four MHD energy fluxes are found. These
values are smaller compared with the value of 4/3 found for hydrodynamic
turbulence. To better understand these results, an in depth analysis is
performed on the total energy flux.
08/2011;
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ABSTRACT: The ideal invariants present in the formalism of magnetohydrodynamics (MHD),
i.e. global quantities that are conserved in the absence of sources and
dissipative effects, play an important role in various theoretical and
numerical studies of MHD turbulence. The fluxes of these ideal invariants
represent separate channels that transfer the information across different
scales in a turbulent system. Once a statistically stationary state of
turbulence is reached, the amount of any ideal invariant quantity introduced in
the system by a forcing mechanism equals the amount of the same quantity
removed by the dissipative effects from the system. For highly developed
turbulence, these two mechanisms act predominantly at different scales that are
largely separated. Since the ideal invariant quantities cascade between scales,
a constant flux is generated with great implication on the state of the system.
Numerically, controlling the ideal invariant fluxes levels for a turbulent MHD
system is important for the analysis of fundamental MHD turbulence properties.
We propose a forcing mechanism that controls the three ideal invariants of MHD
turbulence: the total energy, the cross-helicity and the magnetic helicity.
This forcing is implemented in the freely available TURBO solver, that is also
briefly presented.
08/2011;
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ABSTRACT: The Large Eddy Simulation (LES) approach is adapted to the study of plasma
microturbulence in a fully three-dimensional gyrokinetic system. Ion
temperature gradient driven turbulence is studied with the {\sc GENE} code for
both a standard resolution and a reduced resolution with a model for the
sub-grid scale turbulence. A simple dissipative model for representing the
effect of the sub-grid scales on the resolved scales is proposed and tested.
Once calibrated, the model appears to be able to reproduce most of the features
of the free energy spectra for various values of the ion temperature gradient.
04/2011;
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ABSTRACT: In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.
Physical Review Letters 02/2011; 106(5):055001. · 7.37 Impact Factor
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ABSTRACT: A systematic study of the influence of the viscous effect on both the spectra and the nonlinear fluxes of conserved as well as non conserved quantities in Navier-Stokes turbulence is proposed. This analysis is used to estimate the helicity dissipation scale which is shown to coincide with the energy dissipation scale. However, it is shown using the decomposition of helicity into eigen modes of the curl operator, that viscous effects have to be taken into account for wave vector smaller than the Kolomogorov wave number in the evolution of these eigen components of the helicity. Comment: 6 pages, 2 figures, submited to PoF
09/2010;
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J. Comput. Physics. 01/2010; 229:5862-5869.
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ABSTRACT: A spectral analysis of anisotropic magnetohydrodynamic turbulence, in presence of a constant magnetic field, is presented using high-resolution direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. This decomposition method takes into account the angular dependency of energy transfers in anisotropic systems, while it allows one to recover easily the known shell-to-shell energy transfers in the limit of isotropic turbulence. For large values of the constant magnetic field, the total-energy transfer appears to be most dominant in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic also appears to be important in redistributing the energy between the velocity and the magnetic fields.
Physical Review E 05/2009; 79(4 Pt 2):046312. · 2.26 Impact Factor
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ABSTRACT: Understanding the existence and the dynamics of the magnetic field of the Earth, of the Sun and, in general, of other celestial
bodies (dynamo effect) remains one of the most challenging problems of classical physics. Analytical approaches of this problem
are extremely complicated while numerical efforts are limited to a range of parameter space that is often quite distant from
the realistic systems. For instance, in certain astrophysical bodies as well as in laboratory experiments, the kinematic viscosity
ν of the fluid is six orders of magnitude smaller than its resistivity η. The two dissipation processes therefore take place
at very different time scales. This property makes direct numerical simulations of dynamo intractable. Due to these reasons,
we resort to simplified models.
12/2008: pages 813-816;
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ABSTRACT: A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest neighbour shells, this procedure reproduces well known models but suggests a reinterpretation of the energy fluxes.
08/2008;
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07/2008: pages 609-611;
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ABSTRACT: High resolution direct numerical simulation (DNS) (512×1024×512) and large-eddy simulation (LES) of a shear-free mixing layer are presented. The geometry of the flow consists of two layers with different turbulence intensities that are in contact and interact through a fairly thin mixing layer. This geometry is used to explore the influence of inhomogeneities in the characteristic length scales, times scales and energy scales on the turbulence properties. Comparison of DNS results is made with the Veeravalli & Warhaft (J.
Fluid
Mech. 207, 191–229, 1989) experiment. The LES is performed on a 32×64×32 grid using an eddy-viscosity model. The use of such a model appears to be justified by the very weak departures from isotropy that are observed in the shear-free mixing layer. The LES predictions are compared with the filtered DNS data and show that the eddy viscosity model performs very well in predicting the energy profile as well as the deviation from Gaussianity in the turbulent velocity field statistics.
Journal of Fluid Mechanics 09/2004; 514:153 - 172. · 2.46 Impact Factor
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ABSTRACT: We consider the case of homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field at low to moderate magnetic Reynolds numbers (by moderate we mean here values as high as 20). When the magnetic Reynolds number is vanishingly small ($R_m \ll 1$), it is customary to simplify the governing magnetohydrodynamic (MHD) equations using what is known as the quasi-static (QS) approximation. As the magnetic Reynolds number is increased, a progressive transition between the physics described by the QS approximation and the MHD equations occurs. We show here that this intermediate regime can be described by another approximation which we call the quasi-linear (QL) approximation. For the numerical simulations performed, the predictions of the QL approximation are in good agreement with those of MHD for magnetic Reynolds number up to $R_m \sim 20$.
Journal of Fluid Mechanics 08/2004; 513:199 - 220. · 2.46 Impact Factor
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ABSTRACT: The numerical large eddy simulation (LES) technique is applied toisotropic magnetohydrodynamic (MHD) turbulence. Two dynamic
MHD subgrid-scale models of gradient diffusion type are presented for this purpose, taking into account the fundamental differences
between the dissipation mechanisms of the velocity and the magnetic field. Additional explicit Gaussian filtering in combination
with the tensor-diffusivity mixed model approach is also considered. The LES method is successfully tested a posteriori on scalar level by comparing the obtained results to data stemming from high-resolution direct numerical simulations of decaying
three-dimensional MHD turbulence.
12/2003: pages 367-378;
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ABSTRACT: We present LES results of the evolution of a decaying magneto hydrodynamic (MHD) mixing layer using dynamic eddy-viscosity subgrid scale models. The LES results are obtained using a spectral code with a 32(exp 3) resolution and are compared to a direct numerical simulation (DNS) with 128(exp 3) Fourier modes. The evolution of the kinetic and magnetic energies is presented and their profiles along the inhomogeneous direction is also discussed.
07/2001;
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ABSTRACT: The numerical large eddy simulation (LES) technique is tested on decaying magnetohydrodynamic (MHD) turbulence. The LES approach allows for a strong reduction in computational cost compared to direct numerical simulations by modeling the effects of the smallest turbulent scales instead of computing them directly. Two small-scale models of eddy-viscosity type are presented for this purpose in combination with a procedure for the self-consistent calculation of the model parameters in the course of the simulation. The method is successfully tested by comparing the obtained results to a high-resolution direct numerical simulation of decaying three-dimensional MHD turbulence. © 2001 American Institute of Physics.
Physics of Plasmas 06/2001; 8(7):3502-3505. · 2.15 Impact Factor
