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Broken Ergodicity in MHD TurbulenceIdeal magnetohydrodynamic (MHD) turbulence may be represented by finite Fourier series, where the inherent periodic box serves as a surrogate for a bounded astrophysical plasma. Independent Fourier coefficients form a canonical ensemble described by a Gaussian probability density function containing a Hermitian covariance matrix with positive eigenvalues. The eigenvalues at lowest wave number can be very small, resulting in a large-scale coherent structure: a turbulent dynamo. This is seen in computations and a theoretical explanation in terms of 'broken ergodicity' contains Taylor s theory of force-free states. An important problem for future work is the case of real, i.e., dissipative flows. In real flows, broken ergodicity and coherent structure are still expected to occur in MHD turbulence at the largest scale, as suggested by low resolution simulations. One challenge is to incorporate coherent structure at the largest scale into the theory of turbulent fluctuations at smaller scales.
Document ID
20100009419
Acquisition Source
Johnson Space Center
Document Type
Other
Authors
Shebalin, John V.
(NASA Johnson Space Center Houston, TX, United States)
Date Acquired
August 25, 2013
Publication Date
January 1, 2010
Subject Category
Mathematical And Computer Sciences (General)
Report/Patent Number
JSC-CN-19975
Meeting Information
Meeting: The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
Location: Dresden
Country: Germany
Start Date: May 25, 2010
End Date: May 28, 2010
Sponsors: American Inst. of Aeronautics and Astronautics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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