An analytical formulation for turbulence kinetic energy added by wind turbines based on large-eddy simulation

Wind turbine wakes are plume-like regions characterized by reduced wind speed and enhanced turbulence kinetic energy (TKE) that form downstream of wind turbines. Numerical mesoscale models, like the Weather Research and Forecasting (WRF) model, are generally effective at reproducing the wind speed deficit but lack skills at simulating the TKE added by wind turbines. Here we propose an analytical formulation for added TKE by a wind turbine that reproduces, via least-squares error parameter fitting, the main features of the three-dimensional structure of added TKE as simulated in previous large-eddy simulation (LES) studies, including a streamwise peak at x= 4D-6D (where D is the turbine diameter), a vertical peak near the upper-rotor region, and an annular Gaussian-like distribution along the rotor edge. Validation of the proposed formulation against independent LES results and wind tunnel observations from the literature indicates a promising performance in the case of a single wind turbine wake. The ultimate goal is to insert the proposed formulation, after further improvements, in the WRF model for use within existing or new wind farm parameterizations.