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

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

1999-12-13

arxiv.org/abs/cond-mat/9912222v2

Phys. Rev. E 61, 6644 (2000)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.61.6644

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\"{\i}ve 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 $\sim t^{1+\xi/2}$. 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.

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