Exploring the Impact of Unsteady Pressure Forcing and Surface Buoyancy on the ABL through a Reduced Mass-Spring-Damper Model

The atmospheric and oceanic boundary layers are dynamical systems with complex characteristics that modulate their mean and turbulence responses to external forcing. These responses become particularly intractable when the forces are unsteady. Unsteadiness primarily emanates from the variability of the large-scale mean horizontal pressure gradient and from the changes in the surface heat flux, yet most previous studies have focused on steady-state conditions. To better understand the dynamics of the unsteady atmospheric boundary layer (ABL), we developed a reduced analytical model for mean wind that is based on the unsteady Reynolds-averaged Navier-Stokes equations and validated it against large eddy simulations (see Momen and Bou-Zeid 2016). The model can predict the time variability of the horizontal wind components that results from changes in horizontal pressure gradients and/or ABL stability (due to changes in surface heat flux). Using the new models, we show that the neutral ABL responds to the exerted external pressure gradient variations through an inertial time scale, which could be characterized by the inverse of the Coriolis frequency. This frequency acts as the natural frequency of the system that either damps or magnifies the energy input from the pressure forcing. The dynamics of the system are therefore analogous to a damped oscillator where inertial, Coriolis, and friction forces mirror the mass, spring and damper respectively. When a steady buoyancy (ranging from strongly stable to strongly unstable conditions) is superposed on the unsteady pressure gradient the same model structure can be maintained, but the damping term in the model, corresponding to friction forces, now needs to account for stability (figure (a)). However, for the reverse case with constant pressure gradient under variable surface heat flux and stability, the analytical model needs to be extended to allow time-variable damper coefficient. This extension is presented and validated against results from a suite of large-eddy simulations. We will also compare our obtained solutions in the non-stationary turbulence conditions with other available analytical solutions (figure (b)). In addition to elucidating the fundamental features of the diurnal cycle and low-level jets, this reduced model can be used for short-term forecasts of wind power production, and in various other meteorological and engineering applications. References: Momen, M., and E. Bou-Zeid, 2016: Large Eddy Simulations and Damped-Oscillator Models of the Unsteady Ekman Boundary Layer. J. Atmos. Sci., 73, 25–40, doi:10.1175/JAS-D-15-0038.1. http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-15-0038.1.