Large-Eddy Simulations and Reduced-Models of the Unsteady and Baroclinic Atmospheric Boundary Layer

Elie Bou Zeid, Associate Professor, Department of Civil and Environmental Engineering , Princeton University

Hopeman 224

Understanding and predicting the flow of air in the atmospheric boundary layer (ABL), and how it transports heat and trace gases, are becoming increasingly critical to a wide range of applications including wind and solar energy, urban design, agriculture, and assessment of climate change impacts and adaptations. These applications all require a level of sophistication and detail in our ability to probe and model the ABL and its interaction with the earth surface that manifestly exceeds our current capabilities. Most studies of the meteorology of that layer continue to focus on the “textbook ABL”, which is barotropic, in (quasi) steady-state, and interacts with a horizontal and homogeneous earth surface; it is evident that the “real-world ABL”, even over flat terrain, rarely meets these simplifying conditions. In this talk, we overview two complicating features that have been largely overlooked thus far despite their ubiquity: baroclinicity and unsteadiness. Large-eddy simulations of ABL flow with a time-varying (unsteady) or height-varying (baroclinic) pressure forcings are analyzed to understand how they modulate the bulk structure (mean fields) and turbulence (higher order moments). 

For the unsteady ABL, starting with the equations of a Reynolds-averaged Ekman boundary layer, we demonstrate that the mean flow can be succinctly modeled as a mass-spring damper system. However, the dynamics of higher order turbulence moments depend on the relative magnitudes of three times scales: the inertial time scale (~ 12 hours in mid latitude), the turbulent time scale (~ 0.5 hours), and the forcing variability time scale (varies depending on meso and synoptic scale dynamics). In particular, turbulence is found to be highly out of equilibrium with the mean flow when the forcing time scale ~ turbulence time scale. The findings are more broadly relevant in oceanic flows (for example under oscillating tides), as well as in unsteady engineering flows such as in reciprocating pumps.

For the baroclinic simulations, the mean flow can also be reasonably approximated using analytical solutions. However, the resulting mean and turbulence profiles are strongly influenced by the strength, and more importantly the direction, of the baroclinicity, and can be vastly different from the classic barotropic case. Baroclinicity also alters the topological properties of the largest turbulent structures. For example, peaks in the turbulent kinetic energy can occur in the middle of the layer rather than near the wall. If erroneously interpreted as pertaining to barotropic ABLs, observational analyses under baroclinic conditions can be highly misleading.