Anisotropies in magnetic eld evolution and local Lyapunov exponents

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic eld embedded in a conducting ow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian ow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the ow eld is speci ed. 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 eld, 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 de ned in Lagrangian coordinates. PACS numbers: 05.60.+w, 05.45.+b, 52.55.Dy, 47.10.+g Typeset using REVTEX