Turbulent transport mechanisms in long-lived stable Ekman layers

Abstract: Direct numerical simulations (DNS) are conducted for long-lived stable atmospheric boundary layers (SABLs) maintained by constant ambient stratification and surface cooling. The study examines how stratification mechanism and strength influence turbulence within a four-dimensional parameter space defined by the stratification perturbation parameter ($\Pi_s$), wind-forcing parameter ($\Pi_w$), Rossby-radius factor ($\Pi_f$), and Prandtl number. A regime map in the $\Pi_s-\Pi_w$ plane identifies linearly stable, very stable, and weakly stable regimes, showing that turbulence sustenance is inherently multi-parametric. At low $\Pi_s$ and high $\Pi_w$, a weakly stable regime with persistent turbulence emerges. The SABL exhibits a multilayered thermal structure-comprising a near-surface stable layer, an intermediate unstable layer, and an overlying inversion-that strengthens with decreasing $\Pi_s$, indicating enhanced downward heat transport. Turbulence statistics reveal weak dependence of the momentum field and turbulent kinetic energy (TKE) on stratification, while buoyancy and turbulent potential energy (TPE) show strong sensitivity due to additional production from turbulent heat flux interacting with ambient stratification. Energy transfer occurs among mean gradients, momentum-buoyancy flux, and TKE-TPE exchange. The turbulent Prandtl number exhibits strong vertical variation, exceeding values typical of nocturnal SABLs, underscoring the limits of constant eddy-diffusivity models. Barycentric anisotropy maps indicate weak near-surface effects but enhanced isotropy aloft. These results motivate improved parameterizations for ambient-stratification-dominated SABLs.