CFD simulation of the stratified atmospheric boundary layer: Consistency between Monin-Obukhov similarity theory and the standard k-ε model

Including thermal stratification in CFD simulations of the atmospheric boundary layer (ABL) flow is important for a wide range of applications, from pollutant dispersion over wind energy farm performance to urban thermal microclimate. One of the most important prerequisites for accurate CFD simulations of thermally stratified ABL flow is horizontal homogeneity. Horizontal homogeneity refers to the absence of unintended streamwise gradients in the approach-flow profiles of mean velocity, turbulence quantities and temperature when flowing from the inlet of the domain to the location of interest in the domain, over uniformly rough level terrain. This paper proposes a generic and consistent solution to maintain horizontal homogeneity in CFD simulations of Monin-Obukhov similarity theory (MOST) based stratified ABL flow. A new description is proposed for the coefficient $C_{\epsilon 3}$, which appears in the buoyancy term in the transport equation of the turbulence dissipation rate. This proposed solution is successfully demonstrated by simulations in an empty domain for four stability conditions (1/L = 1/152.4 m⁻¹, 1/1071.7 m⁻¹, 0 m⁻¹ and -1/296.3 m⁻¹), where the standard k-ε turbulence model with the new $C_{\epsilon 3}$ is shown to well maintain the profiles of U, ε and T with only minor deviations for the k profiles. The performance of the turbulence model with the new $C_{\epsilon 3}$ is also illustrated by the flow around a rectangular building under thermal stratification.