Scaling, Anisotropy, and Complexity in Near-Surface Atmospheric Turbulence

The development of a unified similarity scaling has so far failed over complex surfaces, as scaling studies show large deviations from the empirical formulations developed over flat and horizontally homogeneous terrain as well as large deviations between the different complex terrain data sets. However, a recent study of turbulence anisotropy for flat and horizontally homogeneous terrain has shown that separating the data according to the limiting states of anisotropy (isotropic, two-component axisymmetric and one-component turbulence) improves near-surface scaling. In this paper we explore whether this finding can be extended to turbulence over inclined and horizontally heterogeneous surfaces by examining near-surface scaling for 12 different data sets obtained over terrain ranging from flat to mountainous. Although these data sets show large deviations in scaling when all anisotropy types are examined together, the separation according to the limiting states of anisotropy significantly improves the collapse of data onto common scaling relations, indicating the possibility of a unified framework for turbulence scaling. A measure of turbulence complexity is developed, and the causes for the breakdown of scaling and the physical mechanisms behind the turbulence complexity encountered over complex terrain are identified and shown to be related to the distance to the isotropic state, prevalence of directional shear with height in mountainous terrain, and the deviations from isotropy in the inertial subrange.