https://doi.org/10.5194/wes-2019-74 Preprint. Discussion started: 21 October 2019 c Author(s) 2019. CC BY 4.0 License. Rossby number similarity of atmospheric RANS using limited length scale turbulence closures extended to unstable stratification Maarten Paul van der Laan1, Mark Kelly1, Rogier Floors1, and Alfredo Peña1 1Technical University of Denmark, DTU Wind Energy, Risø Campus, Frederiksborgvej 399, 4000 Roskilde, Denmark Correspondence: Maarten Paul van der Laan (
[email protected]) Abstract. The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models repre- senting the atmospheric boundary layer. In this work we employ one-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmo- 5 spheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited length scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric 10 stabilities. 1 Introduction Wind turbines operate in the turbulent atmospheric boundary layer (ABL) but are designed with simplified inflow conditions that represent analytic wind profiles of the atmospheric surface layer (ASL).