大气流动中的确定性混沌、分形和类量子力学
Deterministic chaos, fractals and quantumlike mechanics in atmospheric flows
摘要：
大气流动的复杂时空模式是由大小从毫米到数千公里不等的波动共同存在所造成的，据发现，这种模式表现出长距离的时空相关性。这些相关性表现为全球云量分布的自相似分形几何和大气涡动能量谱的逆幂律形式。这种长程时空关联在扩展的自然动力系统中普遍存在，是确定性混沌或自组织临界性的标志。本文考虑微观区域涡旋动力学过程，建立了一个大气环流的元胞动力系统模式。这种非确定性模型使得能够制定一个简单的封闭的一组控制方程，用于预测和描述观测到的大气流动结构特征如下。大气流中确定性混沌场的奇异吸引子设计由嵌套的连续对数螺旋环流组成，其描绘出准周期性彭罗斯镶嵌图案，在凝聚态物理中被识别为准晶体结构。大气涡旋能量结构遵循类似于量子力学定律的定律。表征量子力学定律的表观波粒二象性归因于涡旋环流固有的双向能量流中能量显示的双峰现象学形式，例如，上升气流中云的形成和下降气流中云的消散，导致观察到云结构的离散细胞几何形状。
英文摘要：
The complex spaciotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spacial and temporal correlations. These correlations are manifested as the self-similar fractal geometry of the global cloud cover pattern and the inverse power-law form for the atmospheric eddy energy spectrum. Such long-range spaciotemporal correlations are ubiquitous in extended natural dynamical systems and are signatures of deterministic chaos or self-organized criticality. In this paper, a cell dynamical system model for atmospheric flows is developed by consideration of microscopic domain eddy dynamical processes. This nondeterministic model enables formulation of a simple closed set of governing equations for the prediction and description of observed atmospheric flow structure characteristics as follows. The strange-attractor design of the field of deterministic chaos in atmospheric flows consists of a nested continuum of logarithmic spiral circulations that trace out the quasi-periodic Penrose tiling pattern, identified as the quasi-crystalline structure in condensed matter physics. The atmospheric eddy energy structure follows laws similar to quantum mechanical laws. The apparent wave-particle duality that characterize quantum mechanical laws is attributed to the bimodal phenomenological form of energy display in the bidirectional energy flow that is intrinsic to eddy circulations, e.g., formation of clouds in updrafts and dissipation of clouds in downdrafts that result in the observed discrete cellular geometry of cloud structure.
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