湍流连续介质动力学模拟的细胞动力系统模型
A Cell Dynamical System Model for Simulation of Continuum Dynamics of Turbulent Fluid Flows
摘要：
大气流动表现出长距离的时空相关性，表现为全球云量模式的分形几何，伴随着从湍流（毫米-秒）到气候（数千毫秒-年）的所有尺度的时间波动的功率谱的逆幂律形式。长程时空相关性在自然界的动力系统中普遍存在，并被认为是自组织临界性的特征。气象学理论中湍流的标准模型不能满意地解释观测到的大气流动的多重分形（时空）结构。模拟和预测大气流动的数值模型易受确定性混沌的影响，并给出不切实际的解。确定性混沌是迭代计算中舍入误差增长的直接结果。有限精度计算的舍入误差在迭代计算的每一步平均加倍。在长期数值积分方案中包含数千次迭代计算的数值天气预报和气候模式中，舍入误差会传播到主流计算中，并给出不切实际的解。最近发展的非确定性细胞动力系统模型的大气流动预测所观察到的自组织临界性作为内在的量子力学控制流动动力学。此外，弦状大气流轨迹的分形时空结构被分解为一个连续的涡旋。涡旋环流服从开普勒第三行星运动定律，因此涡旋惯性质量在从微观到宏观的所有尺度上都服从牛顿引力平方反比定律。
英文摘要：
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations of all scales ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models for turbulent fluid flows in meteorological theory cannot explain satisfactorily the observed multifractal (space-time) structures in atmospheric flows. Numerical models for simulation and prediction of atmospheric flows are subject to deterministic chaos and give unrealistic solutions. Deterministic chaos is a direct consequence of round-off error growth in iterative computations. Round-off error of finite precision computations doubles on an average at each step of iterative computations. Round-off error will propagate to the mainstream computation and give unrealistic solutions in numerical weather prediction and climate models which incorporate thousands of iterative computations in long-term numerical integration schemes. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics. Further, the fractal space-time structure to the stringlike atmospheric flow trajectory is resolved into a continuum of eddies. The eddy circulations obey Kepler third law of planetary motion and therefore eddy inertial masses obey Newton inverse square law of gravitation on all scales from microscopic to macroscale.
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