大气湍流能量级串的主要模式及其标度律统计特性的比较研究

In the statistical theory of atmospheric turbulence, the scaling law is an important research content in complex nonlinear dynamic systems with multiscale and freedom with large degree, which is regarded as universal scaling law that have nothing to do with the characteristics of large-scale motion, viscous dissipation mechanism as well as unrelated to specific environmental flows. After observed that intermittent and coherent structures in the experiment, the comparative study to each scaling law is required, the focus is on the physical mechanism of statistical methods, that is, what factors dominate or control turbulent energy cascade in inertial range, focus on what kinetic characteristics of energy transmission and dissipation were actually reflected by the scaling law in inertial range. To our knowledge, up to now, the problem is still unclear, and before there is no in-depth study, so, it is worthwhile to research by us. .Because N-S equations contain the nonlinear term , which makes the diversity of results of theoretical studies and numerical experiments, especially, there is no any effective mathematical approach to solve the closure issue. Therefore, we use wavelet transform and Hilbert-Huang transform in the physical space (time domain) and Fourier spectrum analysis in wave number space (wave number domain) to make analysis of important turbulent kinetic energy transport Karman-Horwarth equation, and in order to obtain one pattern of turbulent energy transport, dissipation and rebalancing, which is a clearer pattern than ever one, it can increase our in-depth understanding about the dynamic characteristics in inertial sub-range, especially in-depth understanding intermittency and testing universal scaling law of atmospheric turbulence energy cascade.

在大气湍流的统计理论中，标度律是多尺度、大自由度、复杂非线性动力系统的重要研究内容，具有普适性，它与大尺度的运动特性，粘性耗散机理以及流动的具体环境无关。在实验中观测到间歇性和拟序结构之后，需要对各标度律进行比较研究，重点是其统计方法的物理机制，它们到底反映了惯性副区能量输运和耗散的什么样的动力学特性。直至目前，这个问题仍然是不清楚的，并没有深入研究过，值得我们去探讨。.由于N-S方程中存在的非线性项和不封闭问题，使得理论研究和数值实验的结果具有多样性，还没有任何有效的数学处理方法。为此，我们在物理空间中采用小波变换和Hilbert-Huang变换，在波数空间中采用傅里叶谱分析方法对重要的湍流动能输运的动力学方程进行时域和波数域分析，以获得比以往更清晰的湍能输运、耗散、再平衡的图案，真正实现对标度律普适性的比较和检验，从而增加对大气湍流中能量级串、间歇性和惯性副区的动态特性的深入理解。

在大气湍流的统计理论中，标度律是多尺度、大自由度、复杂非线性动力系统的重要研究内容，具有普适性，它与大尺度的运动特性，粘性耗散机理以及流动的具体环境无关。在实验中观测到间歇性和拟序结构之后，需要对各标度律进行比较研究，重点是其统计方法的物理机制，它们到底反映了惯性副区能量输运和耗散的什么样的动力学特性。直至目前，这个问题仍然是不清楚的，并没有深入研究过，值得我们去探讨。在项目的支持下，我们深入探讨了局部均匀各项同性湍流统计理论中，惯性副区存在间歇性和拟序结构的情况下，能量级串的特征及其影响因素，以及标度律所反映的惯性副区能量输运和耗散的动力学特性。通过分析城市、草原及海洋等不同下垫面的实验数据，采用傅氏变换、小波变换和Hilbert-Huang变换对湍动能输运方程Karman-Horwarth方程进行频谱分析，比较能谱、输运谱和耗散谱的惯性区，验证了拟序结构对其标度律的影响。对惯性区能谱、拟序结构、标度特性的研究目标已经完成。

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