Communications in Mathematical Physics

, Volume 132, Issue 3, pp 519–536 | Cite as

Constrained random walks and vortex filaments in turbulence theory

  • Alexandre Joel Chorin


We consider a simplified model of vorticity configurations in the inertial range of turbulent flow, in which vortex filaments are viewed as random walks in thermal equilibrium subjected to the constraints of helicity and energy conservation. The model is simple enough so that its properties can be investigated by a relatively straightforward Monte-Carlo method: a pivot algorithm with Metropolis weighting. Reasonable values are obtained for the intermittency dimensionD, a Kolmogorov-like exponent γ, and higher moments of the velocity derivatives. Qualitative conclusions are drawn regarding the origin of non-gaussian velocity statistics and regarding analogies with polymers and with systems near a critical point.


Polymer Vortex Neural Network Statistical Physic Vorticity 


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© Springer-Verlag 1990

Authors and Affiliations

  • Alexandre Joel Chorin
    • 1
  1. 1.Department of MathematicsUniversity of California and Lawrence Berkeley LaboratoryBerkeleyUSA

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