Mean and turbulence dynamics in unsteady Ekman boundary layers

Abstract

Unsteady pressure gradients in turbulent flows not only influence the mean, but also affect the higher statistical moments of turbulence. In these flows, it is important to understand if and when turbulence is in quasi-equilibrium with the mean in order to better capture the dynamics and develop effective closure models. Therefore, this study aims to elucidate how turbulence decays or develops relative to a time-varying mean flow, and how the turbulent kinetic energy (TKE) production, transport and dissipation respond to changes in the imposed pressure forcing. The focus is on the neutral unsteady Ekman boundary layer, where pressure-gradient, Coriolis and turbulent friction forces interact, and the analyses are based on a suite of large-eddy simulations with unsteady pressure forcing. The results indicate that the dynamics is primarily controlled by the relative magnitudes of three time scales: the inertial time scale (characterized by Coriolis frequency ${\sim}12$ hours at mid-latitudes), the turbulent time scale (${\sim}2$ hours for the largest eddies in the present simulations) and the forcing variability time scale (which is varied to reflect different (sub)meso to synoptic scale dynamics). When the forcing time scale is comparable to the turbulence time scale, the quasi-equilibrium condition becomes invalid due to highly complex interactions between the mean and turbulence, the velocity profiles manifestly depart from the log-law and the normalized TKE budget terms vary strongly in time. However, for longer, and surprisingly for shorter, forcing times, quasi-equilibrium is reasonably maintained. The analyses elucidate the physical mechanisms that trigger these dynamics, and investigate the implications on turbulence closure models.

Spatial constraints in large-scale expansion of wind power plants

“…They highlighted that, given a wind forcing, the earliest response is driven by diffusive momentum transfer, followed by the Coriolis acceleration, and lastly by inertial oscillations that slowly decay. Momen and Bou-Zeid (33,34) studied by means of large-eddy simulations the unsteady Ekman layer under sinusoidal pressure forcing, and identified two characteristic timescales, an inertial and a turbulent timescale. They also demonstrated that, under certain regimes, the unsteady Ekman layer behaves as a dynamic second-order system (i.e., a mass-spring-damper system), in which the mass corresponds to the flow inertia, the spring to the conservative Coriolis force, and the damper to the frictional dissipation.…”

Influence of the geostrophic wind direction on the atmospheric boundary layer flow

“…More recent studies of the moderate Reynolds number turbulent Ekman layer have continued to neglect the horizontal component of Earth's rotation (see e.g. Momen & Bou-Zeid (2017) and Gohari & Sarkar (2018)). Meanwhile, neglecting the horizontal component of Earth's rotation has been shown to be invalid in oceanic flows (Gerkema & Shrira 2005;Gerkema et al 2008;Grisouard & Thomas 2015;Delorme & Thomas 2019).…”

Baroclinicity and directional shear explain departures from the logarithmic wind profile

“…In itself, the assumption that Ro is the only external parameter restricts the similarity theory to a steady‐state, neutral, and barotropic ABL (mean pressure gradients or geostrophic winds do not vary with height). Among other common departures from this idealization, such as unsteadiness (e.g., Momen and Bou‐Zeid, 2016; 2017; Pan and Patton, 2017; Cava et al ., 2019) and/or buoyancy (e.g., Salesky et al ., 2013; Ghannam et al ., 2017), the effects of baroclinicity on the wind and stress profiles remain poorly studied. Baroclinicity arises from large‐scale horizontal temperature gradients, leading to height‐dependent atmospheric pressure gradients from the thermal wind balance.…”