Zoom on vorticity
Local Beltramization (Tsinober & Levich (1983); Moffatt (1985); Farge et al. (2001); Holm & Kerr (2002))
> Role of helicity at small scales and slow return to isotropy

Relative helicity (95% level)
Relative Helicity: Blue h> 0.95
Red h<0.95

Zoom on two regions of strong current density, and magnetic field lines in their vicinity (in brown) for a run with initial conditions that are random with a largescale Beltrami flow. We integrate the magnetohydrodynamic equations on a grid of
1536x1536x1536 regularly spaced points, using a dealiased pseudospectral method.
The current sheets are thin and elongated (up to 1/3 the size of the box); the magnetic field lines are parallel to the sheet and quasiorthogonal to each other on each side of it, and they depart from the sheet transversally. Both folding (left) and rolling (right) occurs at this Reynolds number. Vortex sheets (not shown) are colocated and parallel to the current sheets. Computations done at NCAR by Pablo Mininni ; the VAPOR visualization software is developed at NCAR.
In collaboration with Pablo Mininni and David Montgomery (Dartmouth).

Collision of two shocks in a diagonal onedimensional advection diffusion equation, shown (a) at early times, (d) at intermediate times and (f) close to the time of maximum steepness of the shock. The code is an adaptive mesh refinement code using spectral elements (with p=8 in all elements. More information on the GASpAR code (Geophysical Astrophysical SPectral element Adaptive Refinement) can be found on the web). A movie of the coalescence of three vortices for the twodimensional NavierStokes equations, together with the corresponding energy spectra can be found at www.image.ucar.edu/~fournier/projects/nug3vort.
(see [97], in collaboration with Aimé Fournier and Duane Rosenberg (NCAR)).

Critical magnetic Reynolds number for dynamo action as a function of inverse magnetic Prandtl number PM. As PM decreases, the magnetic field line stretching has to overcome the complexity of the flow that develops as it becomes more turbulent. The forcing is the TaylorGreen von Karman flow corresponding to two counterrotating cylinders, a configuration widely used in the laboratory. Three numerical methods are employed to achieve this result: direct numerical simulations at PM~1, Lagrangian averaged model for intermediate values of PM and Large Eddy Simulations at the lowest values of PM. Similar results hold for other type of forcing, and PM~0.002 can be reached in that fashion, much lower than what was previously obtained but still at least two orders of magnitude away from laboratory values for liquid metals, for the liquid core of the Earth or for the solar convection zone.
Work done in collaboration with Pablo Mininni (NCAR), David Montgomery (Dartmouth), JeanFrançois Pinton (ENS Lyon), Hélène Politano (OCANice) and Yannick Ponty (OCANice).

Variation with wavenumber of the ratio of energy flux coming from the large scales to the energy flux from all scales for increasing Reynolds numbers Re; dashdot line, Re~675, dash line, Re~875, and solid line, Re~3950; the corresponding Taylor Reynolds numbers are respectively 300, 350 and 800; the forcing is a Taylor Green flow.
Note that, only for the highest resolution run, there is a wavenumber range where this ratio becomes constant. The question arises as to how this ratio evolves with Reynolds number; a run at Pittsburgh on a grid of more than 8 billions points is being done presently in an attempt to find out.
(see reference #[101], in collaboration with Alexandros Alexakis (OCA, Nice) and Pablo Mininni (NCAR).

Comparison of three computations in twodimensional MHD turbulence:
the solid line is a direct numerical simulation and the two other lines are for two runs using the Lagrangian Averaged alpha model with two different filter lengths (vertical arrows in the graph). What is plotted is the relative energy E_R, i.e. the difference between the magnetic and kinetic energy. The amount of E_R in the small scales was shown to be proportional to a (negative when there is more magnetic
energy) turbulent resistivity responsible for the inverse cascade of magnetic potential (see ref. 10). The models fail to reproduce this result, and hence the magnetic potential undergoes a weaker inverse cascade (see ref. [87]).
In collaboration with Pablo Mininni and David Montgomery


MHD Turbulence structures
_256^3 simulation.
_Regions with strong gradients (current sheets) are generated as the system evolves.
_Current sheets separate regions with magnetic field lines pointing in opposite directions.
_Later, the current sheets break down and a turbulent regime is reached.
_No vortex tubes can be recognized.
_Is the fast generation of these structures associated with nonlocal effects in MHD?

Zoom on vortex tubes with helical field lines
Note intertwining of tubes (Vapor software, NCAR)
Role of helicity ? 