Beyond the Textbook EBL: Mean and Turbulence in Unsteady Ekman Boundary Layers

The quasi-steady state assumption in geophysical boundary layers is often used, but its validity and limitations are rarely investigated. Unsteady geostrophic forcing in the atmosphere or ocean challenges this assumption, and can strongly influence the mean wind and higher order turbulence statistics. Under such conditions, it is important to understand when and if turbulence can be considered in quasi-equilibrium, and what are the implications of unsteadiness and disequilibrium on flow characteristics and on the classic equilibrium-based models. To that end, one needs to understand how the turbulence decays or develops, and how the turbulent production, transport and dissipation respond to changes in the imposed forcing. The knowledge obtained from studying these questions help us understand the underlying fundamental physical dynamics of the unsteady boundary layers, and develop better turbulence closures for weather/climate models and engineering applications. The present study focuses on the unsteady Ekman boundary layer (EBL) where pressure gradient forces, Coriolis forces, and turbulent friction forces interact but are not necessarily in equilibrium. We perform a suite of large eddy simulations with variable forcing and acquire the corresponding turbulence statistics such as the resolved turbulent kinetic energy budget terms. The results indicate that the dynamics are primarily controlled by the relative magnitudes of three time scales: the inertial time scale (τ_EBL), the turbulent time scale ( τ_t ~ 2 hours or less in the simulations), and the forcing variability time scale (τ_f which is varied to reflect different (sub)meso- to synoptic-scale dynamics). Several cases with unsteady geostrophic forcing ranging from very fast to slow oscillations are simulated to examine how the turbulence is modulated by the variability of the mean pressure gradient. We investigate the influence of the forcing variability time scale on the turbulence equilibrium and TKE budget, and assess the implications for mean-turbulence nonlinear interactions and turbulence modeling in such flows. Furthermore, the logarithmic wind profile validity in an unsteady framework is examined. It is shown here that when the forcing time scale is on the order of the turbulence characteristic time scale (figure (b)), the turbulence is no longer in the quasi-equilibrium state due to highly complex mean-turbulence interactions and hence the conventional log-law and turbulence closures are no longer valid in these conditions. However, for longer (figure (a)) and, surprisingly, for shorter forcing times (figure (c)) quasi-equilibrium is maintained.