E1. Mean Velocity Profile in a Sheared and Thermally Stratified Atmospheric Boundary Layer

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Most human activity and biological processes occur within the lower atmosphere, a thermally stratified region characterized by shear and buoyancy-driven turbulence. Thermal stratification arises because of diurnal heating and cooling resulting in finite sensible heat flux at the Earth’s surface, while turbulence is mechanically produced due to the reduced mean velocity near the ground. The coexistence of shear- and buoyancy-generated turbulence leads to many difficulties in describing the flow properties in the lower atmosphere. Even for a stationary, horizontally homogeneous, high Reynolds number flow above an infinite flat and heated (or cooled) surface, the description of elementary flow statistics such as the mean velocity profile (MVP) has resisted complete theoretical treatment. There are inklings of a possible universal behavior in the MVP across a wide range of thermal stratification conditions as demonstrated by the collapse of data from multiple field experiments using dimensional analysis, known as Monin-Obukhov similarity theory. The Monin-Obukhov similarity framework has shaped micrometeorology and surface hydrology for more than 60 years now, and it remains the corner stone of virtually every single textbook on lower-atmospheric turbulence. The stability correction functions (SCF) are used in all climate, atmospheric, air quality, hydrologic, and ecological applications, including models of land-surface processes when land-surface fluxes are to be coupled to the state of the atmosphere. Yet, despite the SCF’s wide usage, even phenomenological theories that predict their canonical shape are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients of MVP already reported from numerous field experiments. When taken together with a similar derivation for Manning’s equation and the Reynolds number dependence of the Nikuradse friction-factor, a blueprint for a unifying theory that bridges the Kolmogorov turbulent kinetic energy spectrum to widely used empirical results describing high Reynolds number flows in hydrology is beginning to unfold.

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