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

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 N approximately t(-xi), with xi approximately 1 instead of the value xi=4/3 predicted by a naive kinetic theory. For short time, we find an effective exponent xi approximately 0.7 consistent with previous simulations and experiments. We show that the mean square displacement of surviving vortices grows as approximately t(1+xi/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 xi=1. We find that the theoretical relations between kinetic parameters are all in good agreement with experiments.