Mathematical estimates for the attractor dimension in MHD turbulence

@inproceedings{Pothrat2003MathematicalEF,
  title={Mathematical estimates for the attractor dimension in MHD turbulence},
  author={Alban Poth{\'e}rat and Thierry Alboussi{\`e}re},
  year={2003}
}
The aim of the present work is to derive rigorous estimates for turbulent MHD flow quantities such as the size and anisotropy of the dissipative scales, as well as the transition between 2D and 3D state. To this end, we calculate an upper bound for the attractor dimension of the motion equations, which indicates the number of modes present in the fully developed flow. This method has already been used successfully to derive such estimates for 2D and 3D hydrodynamic turbulence as a function of… 

Figures from this paper

References

SHOWING 1-9 OF 9 REFERENCES
Why, how, and when, MHD turbulence becomes two-dimensional
A description of MHD turbulence at low magnetic Reynolds number and large interaction parameter is proposed, in which attention is focussed on the role of insulating walls perpendicular to a uniform
Determining modes and fractal dimension of turbulent flows
Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments,
Attractor dimension and small length scale estimates for the three-dimensional Navier - Stokes equations
It is shown that a rigorous estimate for the fractal dimension of the global attractor of the three-dimensional incompressible Navier - Stokes equations on periodic boundary conditions is given by
Attractors Representing Turbulent Flows
Attractor dimension and small scales estimates for the three dimensional navier-stokes equations. non linearity
  • 1997
Local structure of turbulence in an incompressible fluid at very high reynolds numbers
  • Dokl. Akad. Nauk. SSSR,
  • 1941
Alboussière. Small scales and anisotropy in low
  • Rm MHD turbulence. Phys. Fluids,
  • 2003