Breakdown of the velocity and turbulence in the wake of a wind turbine – Part 2: Analytical modeling

Abstract. This work aims at developing an analytical model for the velocity and turbulence in the wake of a wind turbine that takes meandering into account and where the expansion and the meandering of the wake can be independently calibrated. The velocity and turbulence breakdown presented in the companion paper allows a better interpretation of the physical phenomena at stake and facilitates the modelling, in particular when it comes to wakes in non-neutral atmosphere. A model for the dominating terms of these breakdowns is here proposed, using only five input parameters: the widths (in vertical and horizontal directions) of the non-meandering wake, the standard deviation of wake meandering (in both directions) and a mixing length. This model can be used either in the FFOR for a static approach or in the MFOR combined with the dynamic wake meandering model for an unsteady approach. The resulting shapes are tested on a neutral and an unstable LES dataset that was computed with Meso-NH. The model shows good results for the axial velocity in both directions. For the axial turbulence, the horizontal profiles are satisfying but further research is needed on the treatment of shear and the parametrisation of the missing terms to better reproduce the vertical asymmetry.