论文标题

拓扑涡流,渐近自由和多重分子

Topological vortexes, asymptotic freedom, and multifractals

论文作者

Migdal, Alexander

论文摘要

我们研究了Kelvinons:Euler方程的单极环溶液,将粘性芯中的汉堡涡流正规化。在无粘性极限中存在有限的异常耗散。但是,在异常的哈密顿式学位中,某些术语正在增长,因为雷诺数的对数。这些术语来自汉堡涡流的核心。在我们的理论中,湍流的多重现象类似于QCD中的渐近自由,这些对数术语以RG方程为总结。小的有效耦合并不意味着较小的速度。相反,与其波动相比,速度很大,这为定量理论开辟了道路。 在扰动理论中的领先顺序中,在这个有效的耦合常数中,我们计算出高速循环矩的多型尺寸,与量子湍流的数据和可用数据符合经典湍流。分形维度对环大小的对数依赖性来自异常尺寸的运行耦合。在现代DNS可以实现的雷诺数字上,分形维度的这种缓慢的对数漂移几乎无法观察到。

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

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