标题： 二维衰减湍流中涡旋聚类的数值重整化群：三体相互作用的作用 显示英文标题

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

摘要： 在本文中，我们介绍了一种数值重整化群过程，该过程允许对二维衰减湍流中的涡旋动力学和合并进行长时间模拟。 涡旋的数量按 $N\sim t^{-\xi}$降低，其中 $\xi\approx 1$代替了由朴素动力学理论预测的值 $\xi=4/3$。 对于短时间，我们发现一个有效的指数 $\xi\approx 0.7$，与之前的模拟和实验一致。 我们表明，存活涡旋的均方位移按 $<x^2>\sim t^{1+\xi/2}$增长。 引入双体和三体碰撞的有效动力学，我们证明只有后者在小涡旋面积覆盖率下变得相关。 与这种机制一致的动力学理论导致 $\xi=1$。 我们发现动力学参数之间的理论关系都与实验高度一致。 显示英文摘要

摘要： 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 $<x^2>\sim t^{1+\xi/2}$. 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.