Turbulent Prandtl number in the atmospheric boundary layer - where are we now?

First-order turbulence closure schemes continue to be work-horse models for weather and climate simulations. The turbulent Prandtl number, which represents the dissimilarity between turbulent transport of momentum and heat, is a key parameter in such schemes. This paper reviews recent advances in our understanding and modeling of the turbulent Prandtl number in high-Reynolds number and thermally stratified atmospheric boundary layer (ABL) flows. Multiple lines of evidence suggest that there are strong linkages between the mean flow properties such as the turbulent Prandtl number in the atmospheric surface layer (ASL) and the energy spectra in the inertial subrange governed by the Kolmogorov theory. Such linkages are formalized by a recently developed cospectral budget model, which provides a unifying framework for the turbulent Prandtl number in the ASL. The model demonstrates that the stability-dependence of the turbulent Prandtl number can be essentially captured with only two phenomenological constants. The model further explains the stability- and scale-dependences of the subgrid-scale Prandtl number in large-eddy simulation. The connections between mean flow properties and microscale energy distributions shed novel insights into the breakdown of Monin-Obukhov similarity theory under strongly stable conditions.