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

Authors
Publication Date
Jan 01, 2000
Source
HAL
Keywords
Language
English
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.