论文标题
-5/3湍流级联的临界和分形结构
Criticality and the fractal structure of -5/3 turbulent cascades
论文作者
论文摘要
在这里，我们展示了一种生成分析结构的程序，该结构产生了级联，该级联反向各向同性均质湍流中的能量谱。我们获得了一个在级联的起源处揭示非自我相似的分形的函数。它揭示了基础$ -5/3 $ cascades的骨干是由确定性嵌套多项式形成的，其中带有HOPF分叉关键点的参数。可以从确定性的低维非线性动力学中获得级联比例（不是通过数值模拟）。因此，对于流体而言，它不应是独有的，而应存在于其他复杂现象中。在确定性和随机情况下都可以获得缩放。
Here we show a procedure to generate an analytical structure producing a cascade that scales as the energy spectrum in isotropic homogeneous turbulence. We obtain a function that unveils a non-self-similar fractal at the origin of the cascade. It reveals that the backbone underlying $-5/3$ cascades is formed by deterministic nested polynomials with parameters tuned in a Hopf bifurcation critical point. The cascade scaling is exactly obtainable (not by numerical simulations) from deterministic low dimensional nonlinear dynamics. Consequently, it should not be exclusive for fluids but also present in other complex phenomena. The scaling is obtainable both in deterministic and stochastic situations.
