Beyond Monin-Obukhov Similarity Theory and the Hockey-Stick Transition

Monin-Obukhov Similarity Theory (MOST) is the canonical theory of boundary layer meteorology and describes the structure of the Atmospheric Surface Layer (ASL). The theory results in the stability functions which relate the non-dimensional local gradient to the Monin-Obukhov stability parameter. In the near-neutral limit MOST converges to the logarithmic wind profile of von Karman and Prandtl. Although MOST is still widely used, limitations have been clear for decades. In the very stable conditions, the surface scaling regime of MOST is replaced by the local scaling regime of Nieuwstadt (1984). More recently, it has been clear that non-local, finite-sized eddies have a large influence on the surface fluxes, even during near-neutral and stably stratified conditions. A local theory, which uses the local gradients, cannot describe all the properties of the ASL. The most significant work on the topic comes from the Hockey-Stick Transition (HOST), developed by Sun et al. (2012). HOST demonstrates two regimes where turbulence first scales with the local gradient until a threshold wind speed is reached, after which the turbulence scales with the wind speed. These features cannot be derived from MOST. Multiple studies have considered how to merge MOST and HOST with some success (e.g. Sun et al. 2020; Grisogono et al. 2020)

In this talk, I will develop the regimes of validity of MOST and HOST using a multitude of datasets measuring the ASL from near-neutral to very stable conditions. I will describe how the different theories differ and in which way they are consistent. The role of bulk shear and finite eddies are discussed illustrating the non-local structure of the ASL and its influence on the associated surface fluxes. I will consider for which scales a finite eddy is active or inactive in the surface fluxes and how it relates to Townsends attached-eddy hypothesis. The talk will end with a prognostic of where improvements and progress is likely to occur.