Anisotropies in magnetic field evolution and local Lyapunov exponents | Zendy

Xian-Zhu Tang | Zendy; Allen H. Boozer | Zendy

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Anisotropies in magnetic field evolution and local Lyapunov exponents

Author(s) -

Xian-Zhu Tang,

Allen H. Boozer

Publication year - 2000

Publication title -

physics of plasmas

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.75

H-Index - 160

eISSN - 1089-7674

pISSN - 1070-664X

DOI - 10.1063/1.873919

Subject(s) - lyapunov exponent , physics , anisotropy , classical mechanics , lorentz transformation , eulerian path , flow (mathematics) , lorentz force , magnetic field , mathematical analysis , reference frame , statistical physics , mechanics , mathematical physics , lagrangian , mathematics , quantum mechanics , frame (networking) , nonlinear system , telecommunications , computer science

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates.

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