Multi-point Monin-Obukhov similarity in the atmospheric surface layer

The Monin-Obukhov similarity hypothesis (MOST) is the theoretical foundation for understanding the atmospheric surface layer. However, it has long been recognized that some important statistics do not follow MOST, indicating incomplete similarity. We propose a generalized MOST, termed multi-point Monin-Obukhov similarity (MMO), hypothesizing that (1) the surface layer has complete similarity, which however can only be represented by multi-point statistics, requiring a horizontal characteristic length scale, which is absent in MOST; (2) The Obukhov length, $L$ is this length scale; (3) All non-dimensional surface-layer multi-point statistics, depend only on the non-dimensional height and separations between the points. The similarity properties (or a lack thereof) for one-point statistics (MOST) can be derived from those of multi-point statistics. A key aspect of the MMO is that at heights much smaller than $-L$ in the convective surface layer, both shear and buoyancy can be important. When applied to the two-dimensional horizontal turbulence spectra, MMO predicts a two-layer structure with three scaling ranges. MMO provides a new framework for analyzing the turbulence statistics and for understanding the dynamics in the atmospheric surface layer.