Bernard Knaepen

Publications (6)0 Total impact

• Chapter: Energy Fluxes and Shell-to-Shell Transfers in MHD Turbulence

  Daniele Carati, Olivier Debliquy, Bernard Knaepen, Bogdan Teaca, Mahendra Verma
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  ABSTRACT: 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.
  07/2007: pages 401-412;
• Chapter: Modelling of MHD Turbulence

  Bernard Knaepen, Olivier Debliquy, Daniele Carati, Sergei Molokov, René Moreau, Keith Moffatt
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  ABSTRACT: Numerical simulations of turbulent phenomena in fluids have made considerable progress with the emergence of large parallel computers. For simple geometries, very efficient numerical methods have been developed to provide accurate numerical solutions to the equations of fluid dynamics. These approaches are referred to as direct numerical simulation (DNS) and their predictions are often regarded as almost as reliable as the experimental data.
  12/2006: pages 247-262;
• Source

  Available from: arxiv.org

  Chapter: Statistical Properties of Dissipative MHD Accelerators

  Kaspar Arzner, Loukas Vlahos, Bernard Knaepen, Nicolas Denewet
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  ABSTRACT: We use exact orbit integration to investigate particle acceleration in a Gauss field proxy of magnetohydrodynamic (MHD) turbulence. Regions where the electric current exceeds a critical threshold are declared to be ‘dissipative’ and endowed with super-Dreicer electric field E Ω = η j. In this environment, test particles (electrons) are traced and their acceleration to relativistic energies is studied. As a main result we find that acceleration mostly takes place within the dissipation regions, and that the momentum increments have heavy (non-Gaussian) tails, while the waiting times between the dissipation regions are approximately exponentially distributed with intensity proportional to the particle velocity. No correlation between the momentum increment and the momentum itself is found. Our numerical results suggest an acceleration scenario with ballistic transport between independent ‘black box’ accelerators.
  02/2006: pages 538-545;
• Source

  Available from: Bogdan Teaca

  Article: Energy transfers in forced MHD turbulence

  Daniele Carati, Olivier Debliquy, Bernard Knaepen, Bogdan Teaca, Mahendra Verma
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  ABSTRACT: The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simu-lations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.
  Journal of Turbulence Volume. 01/2006; 7.
• Source

  Available from: arxiv.org

  Article: The Effect of Coherent Structures on Stochastic Acceleration in MHD Turbulence

  Kaspar Arzner, Bernard Knaepen, Daniele Carati, Nicolas Denewet, Loukas Vlahos
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  ABSTRACT: We investigate the influence of coherent structures on particle acceleration in the strongly turbulent solar corona. By randomizing the Fourier phases of a pseudo-spectral simulation of isotropic MHD turbulence (Re $\sim 300$), and tracing collisionless test protons in both the exact-MHD and phase-randomized fields, it is found that the phase correlations enhance the acceleration efficiency during the first adiabatic stage of the acceleration process. The underlying physical mechanism is identified as the dynamical MHD alignment of the magnetic field with the electric current, which favours parallel (resistive) electric fields responsible for initial injection. Conversely, the alignment of the magnetic field with the bulk velocity weakens the acceleration by convective electric fields $- \bfu \times \bfb$ at a non-adiabatic stage of the acceleration process. We point out that non-physical parallel electric fields in random-phase turbulence proxies lead to artificial acceleration, and that the dynamical MHD alignment can be taken into account on the level of the joint two-point function of the magnetic and electric fields, and is therefore amenable to Fokker-Planck descriptions of stochastic acceleration. Comment: accepted for publication in ApJ
  09/2005;
• Article: Large-eddy simulation without filter

  Bernard Knaepen, Olivier Debliquy, Daniele Carati
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  ABSTRACT: An large-eddy simulation (LES) formalism based on sampling operators instead of filters is developed. The major advantage of this approach is that sampling operators commute with the product and their application to nonlinear terms is not at the origin of any closure problem. In absence of filters that smooth out the small scale structures in the flow, the discretization errors in the LES are expected to be important. They must be modelled. The possible confusion between modelling and discretization errors is however avoided since these two effects are identical in the present formalism. A generalized dynamic procedure is proposed for sampling-based LES which allows for model parameter optimization and does not require a detailed analysis of the discretization error. In addition to its interesting mathematical properties for LES, the velocity obtained by a spatial sampling is much closer to experimental probe data than the filtered velocity field.
  Journal of Computational Physics.