In this study, we utilize a novel approach to solve the Ekman equations for eddy-viscosity profiles in the stable boundary-layer. By doing so, a well-known expression for the stable boundary-layer height by Zilitinkevich (Boundary-Layer Meteorology, 1972, Vol. 3, 141–145) is rediscovered.

In this paper, we revisit a well-known formulation of temperature structure parameter ( $$C_T^2$$ C T 2 ), originally proposed by V. I. Tatarskii. We point out its limitations and propose a revised formulation based on turbulence variance and flux budget equations. Our formulation includes a novel physically-based outer length scale which can be estimated from routine meteorological data.

In this study, the stability dependence of turbulent Prandtl number ( $$Pr_t$$ P r t ) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $$Pr_t$$ P...

In this study, we explore several integral and outer length scales of turbulence which can be formulated by using the dissipation of temperature fluctuations ( $$\chi$$ χ ) and other relevant variables. Our analyses directly lead to simple yet non-trivial parameterizations for both spatially-averaged $$\overline{\chi }$$ χ ¯ and the structure parameter of temperature ( $$C_T^2$$ C T 2 ). For our purposes, we make use of high-f...

We use a database of direct numerical simulations to evaluate parametrizations for energy dissipation rate in stably stratified flows. We show that shear-based formulations are more appropriate for stable boundary layers than commonly used buoyancy-based formulations. As part of the derivations, we explore several length scales of turbulence and investigate their dependence on local stability.

We have identified certain fundamental limitations of a mixing-length parametrization used in a popular turbulent kinetic energy-based subgrid-scale model. Replacing this parametrization with a more physically realistic one significantly improves the overall quality of the large-eddy simulation (LES) of stable boundary layers. For the range of grid sizes considered here (specifically, 1 m–12.5 m), the revision dramatically red...