Numerical renormalization group of vortex aggregation in two-dimensional decaying turbulence: The role of three-body interactions

Clément Sire and Pierre-Henri Chavanis
Phys. Rev. E 61, 6644 – Published 1 June 2000
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Abstract

We introduce a numerical renormalization group procedure which permits long-time simulations of vortex dynamics and coalescence in a two-dimensional turbulent decaying fluid. The number of vortices decreases as Ntξ, with ξ1 instead of the value ξ=4/3 predicted by a naïve kinetic theory. For short time, we find an effective exponent ξ0.7 consistent with previous simulations and experiments. We show that the mean square displacement of surviving vortices grows as x2t1+ξ/2. Introducing effective dynamics for two- and three-body collisions, we justify that only the latter become relevant at a small vortex area coverage. A kinetic theory consistent with this mechanism leads to ξ=1. We find that the theoretical relations between kinetic parameters are all in good agreement with experiments.

  • Received 14 December 1999

DOI:https://doi.org/10.1103/PhysRevE.61.6644

©2000 American Physical Society

Authors & Affiliations

Clément Sire* and Pierre-Henri Chavanis

  • Laboratoire de Physique Quantique, UMR C5626 du CNRS, Université Paul Sabatier, 31062 Toulouse Cedex, France

  • *Electronic address: clement@irsamc2.ups-tlse.fr
  • Electronic address: chavanis@irsamc2.ups-tlse.fr

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Issue

Vol. 61, Iss. 6 — June 2000

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