Saturated State of the Nonlinear Small-Scale Dynamo

A. A. Schekochihin, S. C. Cowley, S. F. Taylor, G. W. Hammett, J. L. Maron, J. C. McWilliams

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Abstract

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.

Original languageEnglish (US)
JournalPhysical review letters
Volume92
Issue number8
DOIs
StatePublished - Jan 1 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Hammett, G. W., Maron, J. L., & McWilliams, J. C. (2004). Saturated State of the Nonlinear Small-Scale Dynamo. Physical review letters, 92(8). https://doi.org/10.1103/PhysRevLett.92.084504