Gallo-Méndez Iván, Moya Pablo S
Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
Sci Rep. 2022 Feb 8;12(1):2136. doi: 10.1038/s41598-022-05996-0.
Kappa distributions (or [Formula: see text]-like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and [Formula: see text]-like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by [Formula: see text]-like distributions. We observe a robust relation between the [Formula: see text] parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the [Formula: see text] parameter; namely [Formula: see text]. We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.
卡帕分布（或类[公式：见原文]分布）代表了一个强大的框架，用于使用非广延统计力学来表征和理解具有高自由度的复杂现象，如湍流系统。在此，我们考虑一个基于耦合映射格朗日的模型，以分析湍流及其空间尺度动力学与类[公式：见原文]分布之间的关系。我们生成了流体在每个尺度上的稳态速度分布，并表明生成的分布能很好地用类[公式：见原文]分布拟合。我们观察到系统的[公式：见原文]参数、尺度和雷诺数Re之间存在稳健的关系。特别是，我们的结果表明，湍流水平与[公式：见原文]参数之间存在封闭的标度关系；即[公式：见原文]。我们期望这些结果有助于在不同背景下表征湍流，并且我们的数值预测能通过观测和实验装置进行检验。
