Multi-Point Monin-Obukhov Similarity in the Atmospheric Surface Layer (Invited Presentation)

The Monin-Obukhov similarity theory (MOST) has been the theoretical foundation for understanding the atmospheric surface layer since its inception. However, it has been known since the early 1970s that a number of important surface layer statistics do not conform to MOST, rendering the surface layer similarity in the original MOST framework incomplete, thereby raising questions about the existence of general similarity in the surface layer. We proposed a generalization of MOST, the multipoint Monin-Obukhov similarity (MMO), which overcomes the major limitations of MOST. It hypothesizes that the surface layer turbulence possesses complete similarity. However, the similarity can only be fully represented by mutipoint statistics, which include the necessary length scale information of the turbulent eddies. Using the new physics of the budget equations for the velocity variances gained from the AHATS field measurements, the theory further identifies the Obukhov length as a horizontal characteristic length scale for the surface layer turbulence, which is a key part of the new theory, but is absent in MOST. MMO further hypothesizes that all multipoint statistics achieve surface layer similarity, making the MMO similarity complete. Recently we derived MMO from the Navier Stokes and potential temperature equations for the case of the horizontal Fourier transforms of the velocity and potential temperature, which are equivalent to the two-point differences for horizontal separations. The derivation is essentially a mathematical proof of MMO for the case of two-point horizontal separations, thereby providing strong support to MMO for general separations between multiple points. MMO provides a new framework for understanding and investigating the atmospheric boundary layer. It also has implications for a range of applications where the surface layer turbulence plays a key role, and for understanding multi-scale phenomena in general.