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Scaling laws in the vortex lattice model of turbulence

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Abstract

The lattice vortex model of the intertial range in turbulence theory is reviewed; the model consists of an array of vortex tubes whose axes coincide with the bonds on a regular lattice, subjected to random stretching and successive scaling, and constrained by conservation laws for energy, specific volume, circulation, helicity, and an energy/vorticity relation. The scaling laws for vorticity are examined in detail, a Hausdorff dimension for the “active” portion of the vortex array is calculated, the origin of intermittency is exhibited, and it is pointed out that the Kolmogorov — 5/3 power law already accounts for intermittency effects.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Alexandre Joel Chorin

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  1. Alexandre Joel Chorin
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Communicated by A. Jaffe

Partially supported by the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF0098, and in part by the Office of Naval Research under contract N00014-76-C-0316

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Chorin, A.J. Scaling laws in the vortex lattice model of turbulence. Commun.Math. Phys. 114, 167–176 (1988). https://doi.org/10.1007/BF01218294

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  • DOI: https://doi.org/10.1007/BF01218294

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