Direct numerical simulations of long-lived stable Ekman layers: impact of stratification mechanisms on turbulence

We investigate long-lived stable Ekman layers through direct numerical simulations (DNS), defining three dimensionless parameters (∏_s, ∏_w, and ∏_f) for a fixed Prandtl number Pr=0.71. These parameters delineate "weakly stable" and "very stable" regimes within the atmospheric boundary layer (ABL). We explore two independent stratification mechanisms: surface cooling (G_w) and ambient stratification (N_a²). The parameter ∏_s (=G_w/N_a²) quantifies the relative influence of these stratification mechanisms, while ∏_w=U_g²/(ν N_a), with U_g representing geostrophic wind and ν kinematic viscosity, is a measure of the significance of the flow's kinetic energy relative to its damping by the combined effects of viscosity and ambient stable stratification. Our findings reveal that for a constant ∏_w, an increase in ∏_s transitions the ABL to a "very stable" state, accompanied by turbulence rebirth at higher ∏_s levels. Conversely, maintaining ∏_s while increasing ∏_w intensifies turbulence, characterizing a "weakly stable" ABL and preventing the collapse and resurgence of turbulence. Furthermore, our results indicate that simulations with higher ∏_s require larger computational domains to accurately capture the dynamics of large-scale structures, a factor potentially overlooked in previous studies due to smaller domain sizes.