Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions

Abstract

In this paper, we introduce a numerical renormalization group procedure which permits long-time simulations of vortex dynamics and coalescence in a 2D turbulent decaying fluid. The number of vortices decreases as $N\sim t^{-\xi }$, with $\xi \approx 1$ instead of the value $\xi =4/3$ predicted by a na\"ıve kinetic theory. For short time, we find an effective exponent $\xi \approx 0.7$ consistent with previous simulations and experiments. We show that the mean square displacement of surviving vortices grows as $<x^2>\sim t^{1+\xi /2}$. Introducing effective dynamics for two-body and three-body collisions, we justify that only the latter become relevant at small vortex area coverage. A kinetic theory consistent with this mechanism leads to $\xi =1$. We find that the theoretical relations between kinetic parameters are all in good agreement with experiments.

23 RevTex pages including 7 EPS figures. Submitted to Phys. Rev. E (Some typos corrected; see also cond-mat/9911032)

References in corpus (2)

• Lagrangian Dynamics in High-Dimensional Point-Vortex Systems
• A coalescence model for freely decaying two-dimensional turbulence

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