Wake turbulence modeling in stratified atmospheric flows using a novel k−ℓ model

As turbines continue to grow in hub height and rotor diameter and wind farms grow larger, consideration of stratified atmospheric boundary layer (ABL) processes in wind power models becomes increasingly important. Atmospheric stratification can considerably alter the boundary layer structure and flow characteristics through buoyant forcing. Variations in buoyancy, and corresponding ABL stability, in both space and time impact ABL wind speed shear, wind direction shear, boundary layer height, turbulence kinetic energy, and turbulence intensity. In addition, the presence of stratification will result in a direct buoyant forcing within the wake region. These ABL mechanisms affect turbine power production, the momentum and kinetic energy deficit wakes generated by turbines, and the turbulent mixing and kinetic energy entrainment in wind farms. Presently, state-of-practice engineering models of mean wake momentum utilize highly empirical turbulence models that do not explicitly account for ABL stability. Models also often neglect the interaction between the wake momentum deficit and the turbulence kinetic energy added by the wake, which depends on stratification. In this work, we develop a turbulence model that models the wake-added turbulence kinetic energy, and we couple it with a wake model based on the parabolized Reynolds-averaged Navier–Stokes equations. Comparing the model predictions to large eddy simulations across stabilities (Obukhov lengths) and surface roughness lengths, we find lower prediction error in both power production and the wake velocity field across the ABL conditions and error metrics investigated.