Multi-Point Monin-Obukhov Similarity and its Application to Turbulence Spectra in the Convective Atmospheric Surface Layer

A generalized Monin-Obukhov similarity hypothesis for the atmospheric surface layer is proposed. It employs the Monin-Obukhov length as a length scale in both the horizontal and vertical directions, in contrast to the original Monin-Obukhov similarity. Therefore, the horizontal turbulence scales, which are contained in multi-point statistics, must be explicitly included. The similarity hypothesis is formulated for the joint probability density function (JPDF) of multi-point velocity and temperature differences, and is termed multi-point Monin-Obukhov similarity (MMO). In MMO, the non-dimensional JPDF in the surface layer depends on the separation vectors and the heights from the ground, both non-dimensionalized by the Monin-Obukhov length. A key aspect of MMO is that at heights much smaller than the absolute value of the Monin-Obukhov length, both shear and buoyancy can be important. As an application, MMO is used to predict the two-dimensional horizontal turbulence spectra in the convective surface layer. It predicts a two-layer structure with three scaling ranges. Comparisons of the predicted spectra with those obtained using high-resolution large-eddy simulation show general agreement, supporting MMO. Within MMO, full similarity is only achieved for multi-point statistics, while similarity properties (or a lack thereof) for one-point statistics (the original Monin-Obukhov similarity) can be derived from those of multi-point statistics. MMO provides a new framework for analyzing the turbulence statistics and for understanding the dynamics in the atmospheric surface layer.