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MHD Turbulence between two and three dimensions
Alban Pothérat
Applied Mathematics Research Centre, Coventry University, United Kingdom
Wed, Feb. 10th 2016, 11:15-12:15
SPEC Salle Itzykson, Bât.774, Orme des Merisiers

Abstract :

TOPIC: Fundamentals, MHD turbulence

MHD turbulence in an externally imposed magnetic field has a well-known tendency to two-dimensionality. The underlying mechanisms were extensively studied in ideal configurations where no-slip walls were present.  They involve a competition between diffusion of momentum by the Lorentz force and 3D instabilities. When physical Hartmann walls are present, however, the picture radically changes. Perfect two-dimensionality is never achieved and a myriad of intermediate states exists between two-and three-dimensional turbulence. We were able to characterise them experimentally by means the FLOWCUBE experimental platform (Pothérat & Klein, JFM 2014): unlike in a geometry without walls, the 2D-3D transition is progressive and the state of the flow is governed by the ratio of the Lorentz force diffusion length lz (Sommeria and Moreau, JFM 1982) to the spacing between Hartmann walls h. This ratio controls the ratio of electric current and dissipation in the boundary layers and in the core. Depending on how active  walls regions are, the local Reynolds number is found to obey three different scalings with the forcing applied, that correspond to three different levels of global dissipation. The most spectacular manifestation of this progressive transition is that within a range of intermediate states between 2 and 3 dimensions, the intensity of turbulent fluctuations increases with the intensity of the externally applied magnetic field.

Figure 1: Schematic representation of generic flow configurations in a channel in an external magnetic field. Hartmann layers are represented in light blue, paths of electric current in red (injected to drive the flow), and fluid flow in blue. (a) lz<  (b) lz~ h,  (c) lz>>h



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