Large eddy simulations and reduced models of the unsteady atmospheric boundary layer

Most studies of the dynamics of Atmospheric Boundary Layers (ABLs) have focused on steady geostrophic conditions. However, real-world ABLs are driven by a time-dependent geostrophic forcing that can change at sub-diurnal scales. Hence, to advance our understanding of the dynamics of atmospheric flows, and to improve their modeling, the unsteady cases have to be analyzed and understood. This is particularly relevant to new applications related to wind energy (e.g. short-term forecast of wind power changes). The present study aims to investigate the ABL behavior under variable forcing and to derive a simple model to predict the ABL response under forcing fluctuations. Large eddy simulations are first presented to illustrate the response of the ABL to changes in forcings. Then, a simplified version of the governing Navier-Stokes equations, with the Coriolis force, is derived and tested using LES. The reduced model is analogous to a mass-spring-damper system and this analogy is exploited to explain the physics of the unsteady ABL. Results from the analytical model match the LES simulations well, and together they indicate that the resulting system in underdamped and open the way for inertial oscillations to play an important role in the dynamics. Several simulations with different variable forcing patterns are then conducted to investigate some of the characteristics of the unsteady ABL such as resonant frequency, ABL response time, equilibrium states, etc. The variability of wind velocity profiles and hodographs, turbulent kinetic energy, and vertical profiles of the total stress and potential temperature are examined.