Achieving stationary statistics in LES of thermally stratified atmospheric boundary layers using a control algorithm

Large Eddy Simulations (LES) are very useful to predict turbulent flows within the atmospheric boundary layer (ABL). Specifically, in the area of renewable energy, recent LES studies of interactions between a neutral ABL and large arrays of wind turbines have led to the derivation of novel similarity relations within the surface layer. These relations were based on observations of horizontally averaged vertical profiles of mean flow and turbulent fluxes, and on detailed comparisons of the boundary layer structure with and without wind turbines. Such comparisons required careful averaging, and were facilitated by ensuring full statistical stationarity of the flow. The extension of these similarity relations to stratified ABL with wind turbine arrays is not trivial, since in the case of non-neutral conditions achieving statistically stationary conditions in LES is challenging. For example, the heat flux at the ground forces vertical profiles of (e.g.) mean temperature to vary quite significantly in time (even if the surface temperature is kept constant, the vertical profiles would go transiently to the neutral state). The focus of this work is on using an artificial source (or sink) of heat, in a region located above ABL, that provides the amount of heat necessary to keep the overall temperature field inside the ABL stationary. This is achieved using a PI control algorithm, designed to keep constant the initial horizontally averaged temperature at a specified height and above. Another controller is used to drive the flow using a geostrophic wind that causes the mean velocity to achieve a prescribed direction at a specified height. This is done by controlling a source term (in the form of an additional Coriolis force) in the momentum equations. This term is 'deactivated' once the flow becomes stationary and the geostrophic wind aligns with the desired direction at a given height. A suite of simulations at various resolutions and levels of thermal stratification are presented, and the profiles are compared with standard similarity relations.