Multipoint Monin–Obukhov Similarity and Its Application to Turbulence Spectra in the Convective Atmospheric Surface Layer

Abstract

Abstract 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 multipoint statistics, must be explicitly included. The similarity hypothesis is formulated for the joint probability density function (JPDF) of multipoint velocity and temperature differences and is termed the multipoint Monin–Obukhov similarity (MMO). In MMO, the nondimensional JPDF in the surface layer depends on the separation vectors and the heights from the ground, both nondimensionalized 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 simulations show general agreement, supporting MMO. Within MMO, full similarity is only achieved for multipoint statistics, while similarity properties (or a lack thereof) for one-point statistics (the original Monin–Obukhov similarity) can be derived from those of multipoint statistics. MMO provides a new framework for analyzing the turbulence statistics and for understanding the dynamics in the atmospheric surface layer.