Understanding turbulence rests delicately on the conflict between Kolmogorov’s 1941 theory of nonintermittent, space-filling energy dissipation characterized by a unique scaling exponent and the overwhelming evidence to the contrary of intermittency, multiscaling, and multifractality. Strangely, multifractality is not typically envisioned as a local flow property, variations in which might be clues exposing inroads into the fundamental unsolved issues of anomalous dissipation and finite time blowup. We present a simple construction of local multifractality and find that much of the dissipation field remains surprisingly monofractal à la Kolmogorov. Multifractality appears as small islands in this calm sea, its strength growing logarithmically with the local fluctuations in energy dissipation—a seemingly universal feature. These results suggest new ways to understand how singularities could arise and provide a fresh perspective on anomalous dissipation and intermittency. The simplicity and adaptability of our approach also holds great promise in applications ranging from climate sciences to medical data analysis.

中文翻译：

---

湍流不是均匀多重分形的

对湍流的理解微妙地依赖于柯尔莫哥洛夫 1941 年的非间歇性、空间填充能量耗散理论（以独特的标度指数为特征）与间歇性、多标度和多重分形相反的压倒性证据之间的冲突。奇怪的是，多重分形通常不被认为是一种局部流动特性，其中的变化可能是揭示反常耗散和有限时间爆炸等基本未解决问题的线索。我们提出了局部多重分形的简单构造，并发现大部分耗散场仍然令人惊讶地保持着柯尔莫哥洛夫的单分形。多重分形就像这片平静的海洋中的小岛一样，其强度随着能量耗散的局部波动呈对数增长——这似乎是一个普遍的特征。这些结果提出了理解奇点如何产生的新方法，并为异常耗散和间歇性提供了新的视角。我们的方法的简单性和适应性在从气候科学到医学数据分析的应用中也具有广阔的前景。