Exploring the multi-fractal nature of the air flow and pollutant dispersion in a turbulent urban atmosphere and its implications for long range pollutant transport

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 Holder 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 M O) 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 b . l) over L M O is greater than 15, and at the same time, the ratio of the height above ground of the wind measurements ( z 0) over L M O is higher than 3 (i.e., in stable regime), then the singularity spectra of wind speed time series indicate that the dominant Holder exponent, h max, 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 0 / L M O < 0, the dominant Holder exponent, h max, 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.