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Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence., Comment: 13 pages, 15 figures. Accepted by ApJ

Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence., Comment: 13 pages, 15 figures. Accepted by ApJ

A class of numerical schemes is developed for the study of charged particle transport in complex stationary electromagnetic fields and tested for fields obtained from a numerical solution of the magneto-hydrodynamic equation. The performances of these schemes are evaluated by analyzing the conservation of energy and the statistical properties of the trajectories. Energy conservation is affected by the interpolation technique used to estimate the field value at the particle position. However, the particle transport properties are more robust, except in the limit of low energy when a significant fraction of the particles are trapped. © 2012 EURATOM- Belgian State., SCOPUS: ar.j, info:eu-repo/semantics/published

A class of numerical schemes is developed for the study of charged particle transport in complex stationary electromagnetic fields and tested for fields obtained from a numerical solution of the magneto-hydrodynamic equation. The performances of these schemes are evaluated by analyzing the conservation of energy and the statistical properties of the trajectories. Energy conservation is affected by the interpolation technique used to estimate the field value at the particle position. However, the particle transport properties are more robust, except in the limit of low energy when a significant fraction of the particles are trapped. © 2012 EURATOM- Belgian State., SCOPUS: ar.j, info:eu-repo/semantics/published

The nature of nonlinear interactions in gyrokinetic turbulence, driven by the ion-temperature gradient instability, is investigated using direct numerical simulations in toroidal flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Because of the nontrivial dissipative nature of gyrokinetic turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for gyrokinetics, is not recovered and an accentuated nonlocal behavior of the IR interactions is found instead, in spite of the local energy cascade observed. © 2012 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

The nature of nonlinear interactions in gyrokinetic turbulence, driven by the ion-temperature gradient instability, is investigated using direct numerical simulations in toroidal flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Because of the nontrivial dissipative nature of gyrokinetic turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for gyrokinetics, is not recovered and an accentuated nonlocal behavior of the IR interactions is found instead, in spite of the local energy cascade observed. © 2012 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

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 force, 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 obtained 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 than 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. © 2011 American Institute of Physics., SCOPUS: cp.j, info:eu-repo/semantics/published

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 force, 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 obtained 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 than 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. © 2011 American Institute of Physics., SCOPUS: cp.j, info:eu-repo/semantics/published

SCOPUS: cp.k, info:eu-repo/semantics/published

Le couplage important entre les différentes échelles d’un écoulement est une des caractéristiques prin-cipales des turbulences. Cela est exprimé mathématiquement par les termes non linéaires présents dans les équations d’équilibre de l’écoulement, dominants en dynamique turbulente. En magnétohy-drodynamique (MHD), la force de Lorentz influe sur l’équation de conservation de l’impulsion et le nombre de termes non linéaires passe à quatre au lieu d’un seul pour un fluide non conducteur.L’objectif principal de cette thèse est d’analyser le transport d’énergie inter-échelles en utilisant une simulation numérique directe d’un écoulement turbulent MHD. Les propriétés de localité du transport de l’énergie entre les échelles pour un écoulement anisotropique ou isotropique, généré par la présence d’un champ magnétique constant, sont renforcées. Un objectif secondaire est d’établir un cadre de travail pour l’étude du transport de particules test chargées dans un champ électromagnétique turbu-lent, i.e. généré par le mouvement d’un fluide conducteur, qui possède des structures à plusieurs ordres de grandeur. La structure de la thèse est présentée ci-dessous.Dans la première partie, composée des deux premiers chapitres, l’auteur présente les notions de turbu-lences, aussi bien hydrodynamiques que MHD. Ces deux chapitres sont des synthèses.La deuxième partie est la principale source de nouveaux résultats. Le chapitre 3 présente les méthodes numériques pour la résolution des équations, les méthodes pseudo-spectrales. Un nouveau type de force est introduit, imposant un niveau de dissipation pour tous les invariants. Dans le chapitre 4, il est effectué une analyse du transfert d'énergie entre ordres de grandeur pour les turbulences MHD. Pour explorer ces transferts d'énergie, le domaine spectral est décomposé en une série de coques de même nombre d'onde. Le transfert moyen d'énergie entre ces coques est analysé. Les transferts d'énergie s'avèrent être surtout locaux en ord, Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

The scale locality functions, originally introduced by Kraichnan for hydrodynamic turbulence, are computed from results of direct numerical simulations of forced magnetohydrodynamic turbulence. It is found that asymptotically the dynamics is dominated by local interactions, but the locality is much weaker than in hydrodynamic turbulence, which is characterized by the scaling exponent of 4/3. Specifically, in magnetohydrodynamic turbulence, two distinct exponents are observed, 1/3 and 2/3. Despite that, direct numerical simulation results reported in this paper exhibit strong coupling between large scales from the forcing band and smallest resolved scales because the locality is too weak to achieve decoupling for the numerical resolution available. © 2010 American Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

A method combining the advantages of a priori and a posteriori testing approaches for subgrid-scale models in large-eddy simulation (LES) is proposed. It is implemented with various simple eddy viscosity models for decaying homogeneous turbulence. The method relies on the introduction of a restoring force in addition to the subgrid model. This force maintains the LES velocity field in the vicinity of the filtered velocity obtained from an accurately simulated flow. The analysis of this force provides new diagnostics on the efficiency of the subgrid-scale models. © 2010 American Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

A systematic approach for constructing high order spline interpolation methods is proposed for fields known on regular, rectangular grids. These interpolation methods are tested in tracking trajectories of particles submitted to a force that derives from a potential known on a grid. The interplay between the time advancement scheme and the spatial interpolation is studied in detail and it is shown how the order of the trajectory solver is directly affected by the order of the spline interpolation. It is also shown how an interpolation method that preserves topological properties of physical fields can be better exploited with these higher order spline approximations. © 2009 Elsevier Inc., SCOPUS: ar.j, info:eu-repo/semantics/published

The scale locality functions, originally introduced by Kraichnan for hydrodynamic turbulence, are computed from results of direct numerical simulations of forced magnetohydrodynamic turbulence. It is found that asymptotically the dynamics is dominated by local interactions, but the locality is much weaker than in hydrodynamic turbulence, which is characterized by the scaling exponent of 4/3. Specifically, in magnetohydrodynamic turbulence, two distinct exponents are observed, 1/3 and 2/3. Despite that, direct numerical simulation results reported in this paper exhibit strong coupling between large scales from the forcing band and smallest resolved scales because the locality is too weak to achieve decoupling for the numerical resolution available. © 2010 American Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

A method combining the advantages of a priori and a posteriori testing approaches for subgrid-scale models in large-eddy simulation (LES) is proposed. It is implemented with various simple eddy viscosity models for decaying homogeneous turbulence. The method relies on the introduction of a restoring force in addition to the subgrid model. This force maintains the LES velocity field in the vicinity of the filtered velocity obtained from an accurately simulated flow. The analysis of this force provides new diagnostics on the efficiency of the subgrid-scale models. © 2010 American Institute of Physics., SCOPUS: ar.j, info:eu-repo/semantics/published

A systematic approach for constructing high order spline interpolation methods is proposed for fields known on regular, rectangular grids. These interpolation methods are tested in tracking trajectories of particles submitted to a force that derives from a potential known on a grid. The interplay between the time advancement scheme and the spatial interpolation is studied in detail and it is shown how the order of the trajectory solver is directly affected by the order of the spline interpolation. It is also shown how an interpolation method that preserves topological properties of physical fields can be better exploited with these higher order spline approximations. © 2009 Elsevier Inc., SCOPUS: ar.j, info:eu-repo/semantics/published

Le couplage important entre les différentes échelles d’un écoulement est une des caractéristiques prin-cipales des turbulences. Cela est exprimé mathématiquement par les termes non linéaires présents dans les équations d’équilibre de l’écoulement, dominants en dynamique turbulente. En magnétohy-drodynamique (MHD), la force de Lorentz influe sur l’équation de conservation de l’impulsion et le nombre de termes non linéaires passe à quatre au lieu d’un seul pour un fluide non conducteur.L’objectif principal de cette thèse est d’analyser le transport d’énergie inter-échelles en utilisant une simulation numérique directe d’un écoulement turbulent MHD. Les propriétés de localité du transport de l’énergie entre les échelles pour un écoulement anisotropique ou isotropique, généré par la présence d’un champ magnétique constant, sont renforcées. Un objectif secondaire est d’établir un cadre de travail pour l’étude du transport de particules test chargées dans un champ électromagnétique turbu-lent, i.e. généré par le mouvement d’un fluide conducteur, qui possède des structures à plusieurs ordres de grandeur. La structure de la thèse est présentée ci-dessous.Dans la première partie, composée des deux premiers chapitres, l’auteur présente les notions de turbu-lences, aussi bien hydrodynamiques que MHD. Ces deux chapitres sont des synthèses.La deuxième partie est la principale source de nouveaux résultats. Le chapitre 3 présente les méthodes numériques pour la résolution des équations, les méthodes pseudo-spectrales. Un nouveau type de force est introduit, imposant un niveau de dissipation pour tous les invariants. Dans le chapitre 4, il est effectué une analyse du transfert d'énergie entre ordres de grandeur pour les turbulences MHD. Pour explorer ces transferts d'énergie, le domaine spectral est décomposé en une série de coques de même nombre d'onde. Le transfert moyen d'énergie entre ces coques est analysé. Les transferts d'énergie s'avèrent être surtout locaux en ord, Doctorat en sciences, Spécialisation physique, info:eu-repo/semantics/nonPublished

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

We investigate anisotropic magnetohydrodynamic turbulence, in presence of a constant magnetic field, using direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. For large values of the constant magnetic field, the total energy transfer appears to be dominant in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic field also appears to be important in redistributing the energy between the velocity and the magnetic fields., SCOPUS: cp.p, info:eu-repo/semantics/published

info:eu-repo/semantics/published

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. © 2009 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

Anisotropic stochastic magnetic fields lead to significant changes in the test particle transport as compared to isotropic cases. The analysis of the Langevin equations for the test particles, when considering both the magnetic anlsotropy and the collisions, lead to anisotropic transport ranging from subdiffusion to diffusion. In absence of collisions, the transport is diffusive in all directions but with different diffusion coefficients. In the case of MHD produced fields, the transport in the plane perpendicular to the main magnetic field is strongly reduced, and appears to be almost diffusive while the parallel transport is still in the ballistic regime., SCOPUS: cp.j, info:eu-repo/semantics/published

info:eu-repo/semantics/published

Anisotropic stochastic magnetic fields lead to significant changes in the test particle transport as compared to isotropic cases. The analysis of the Langevin equations for the test particles, when considering both the magnetic anlsotropy and the collisions, lead to anisotropic transport ranging from subdiffusion to diffusion. In absence of collisions, the transport is diffusive in all directions but with different diffusion coefficients. In the case of MHD produced fields, the transport in the plane perpendicular to the main magnetic field is strongly reduced, and appears to be almost diffusive while the parallel transport is still in the ballistic regime., SCOPUS: cp.j, info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high resolution direct numerical simulations of both forced and decaying isotropic turbulence. The triad interactions between velocity and magnetic field modes are averaged into shell interactions between similar length scales phenomena. This is achieved by combining all the velocity Fourier modes that correspond to wave vectors with similar amplitude into a shell velocity variable. The same procedure is adopted for the magnetic field. The analysis of the interactions between these shell variables gives a global picture of the energy transfers between different length scales, as well as between the velocity and the magnetic fields. Also, two different attempts to separate the shell-to-shell interactions into forward and backward energy transfers are proposed. They provide diagnostics that can be used in order to assess subgrid-scale modelling in large-eddy simulation for turbulent MHD systems. © Springer-Verlag Berlin Heidelberg 2007., SCOPUS: ar.k, info:eu-repo/semantics/published

info:eu-repo/semantics/nonPublished

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high resolution direct numerical simulations of both forced and decaying isotropic turbulence. The triad interactions between velocity and magnetic field modes are averaged into shell interactions between similar length scales phenomena. This is achieved by combining all the velocity Fourier modes that correspond to wave vectors with similar amplitude into a shell velocity variable. The same procedure is adopted for the magnetic field. The analysis of the interactions between these shell variables gives a global picture of the energy transfers between different length scales, as well as between the velocity and the magnetic fields. Also, two different attempts to separate the shell-to-shell interactions into forward and backward energy transfers are proposed. They provide diagnostics that can be used in order to assess subgrid-scale modelling in large-eddy simulation for turbulent MHD systems. © Springer-Verlag Berlin Heidelberg 2007., SCOPUS: ar.k, info:eu-repo/semantics/published

info:eu-repo/semantics/nonPublished

info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published