Mouzourides Petros, Kyprianou Andreas, Neophytou Marina K-A
Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, School of Engineering, University of Cyprus, Nicosia 2109, Cyprus.
Department of Mechanical and Manufacturing Engineering, School of Engineering, University of Cyprus, Nicosia 2109, Cyprus.
Chaos. 2021 Jan;31(1):013110. doi: 10.1063/1.5123918.
This work investigates the multi-fractal nature of a turbulent urban atmosphere using high-resolution atmospheric data. Meteorological and concentration measurements of passive and reactive pollutants collected over a 3-year period in a sub-urban high-Reynolds number atmospheric field were analyzed. Scaling laws characterizing the self-similarity and thereby depicting the multi-fractal nature are determined by calculating the singularity spectra, where a range of Hölder exponents, h, are estimated. In doing so, the complexity of the urban atmosphere entailing different stability regimes was addressed. Using the Monin-Obukhov length (L) as a marker of atmospheric stability and thereby an indication of the magnitude of anisotropy, we find where and how self-similarity is manifested relative to the different regimes and we estimate corresponding appropriate scaling laws. We find that the wind speed obeys the -5/3 law suggested by Kolmogorov only when the atmosphere lies within the stable regime as defined by Monin-Obukhov theory. Specifically, when the ratio of the atmospheric boundary layer height (H) over L is greater than 15, and at the same time, the ratio of the height above ground of the wind measurements (z) over L is higher than 3 (i.e., in stable regime), then the singularity spectra of wind speed time series indicate that the dominant Hölder exponent, h, coincides with Kolmogorov's second hypothesis. On the contrary under unstable regimes in the atmosphere where the anisotropy is approached, different scaling laws are estimated. In detail, when z/L<0, the dominant Hölder exponent, h, of the singularity spectra of the wind speed time series is either negative or close to zero, which is an indication of an impulse-like singularity, that is associated with rapid changes. For the ambient temperature and air quality measurements such as of carbon monoxide and particulate matter concentrations, it was found that they obey different laws, which are related with the long-term correlation of their data fluctuation.
本研究利用高分辨率大气数据，对湍流城市大气的多重分形性质展开调查。分析了在一个城郊高雷诺数大气场中，历时3年收集的气象数据以及被动和活性污染物的浓度测量数据。通过计算奇异谱来确定表征自相似性并进而描绘多重分形性质的标度律，其中估计了一系列的赫尔德指数h。在此过程中，探讨了包含不同稳定状态的城市大气的复杂性。以莫宁-奥布霍夫长度（L）作为大气稳定性的标志，从而作为各向异性大小的一个指标，我们发现了自相似性相对于不同状态在何处以及如何表现出来，并估计了相应合适的标度律。我们发现，只有当大气处于莫宁-奥布霍夫理论所定义的稳定状态时，风速才遵循柯尔莫哥洛夫提出的-5/3律。具体而言，当大气边界层高度（H）与L的比值大于15，同时风速测量高度（z）与L的比值高于3时（即处于稳定状态），风速时间序列的奇异谱表明，主导赫尔德指数h与柯尔莫哥洛夫的第二个假设相符。相反，在大气不稳定状态下，当接近各向异性时，会估计出不同的标度律。详细来说，当z/L<0时，风速时间序列奇异谱的主导赫尔德指数h为负或接近零，这表明存在类似脉冲的奇异性，与快速变化相关。对于环境温度和空气质量测量，如一氧化碳和颗粒物浓度，发现它们遵循不同的规律，这与它们数据波动的长期相关性有关。
