31 May 2022
 | 31 May 2022
Status: this preprint is currently under review for the journal WES.

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

Erwan Jézéquel, Frédéric Blondel, and Valéry Masson

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.

Erwan Jézéquel et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2022-47', Anonymous Referee #1, 24 Jun 2022
    • AC1: 'Comment on wes-2022-47', Erwan Jézéquel, 19 Aug 2022
  • RC2: 'Comment on wes-2022-47', Anonymous Referee #2, 28 Jun 2022
    • AC1: 'Comment on wes-2022-47', Erwan Jézéquel, 19 Aug 2022
  • AC1: 'Comment on wes-2022-47', Erwan Jézéquel, 19 Aug 2022

Erwan Jézéquel et al.

Data sets

Figures data from papers "Breakdown of the velocity and turbulence in the wake of a wind turbine", parts 1 and 2 Erwan Jézéquel

Model code and software

Implementation of the analytical model deduced from the velocity and turbulence breakdown Erwan Jézéquel, Frederic Blondel

Erwan Jézéquel et al.


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Short summary
Analytical models allow to compute quickly the decreased power output and lifetime induced by wakes in a wind farm. This is achieved by evaluating the modified velocity and turbulence in the wake. In this work, we present a new model based on the velocity and turbulence breakdowns presented in part 1. This new model is physically based, allows to compute the whole turbulence profile (rather than the maximum value) and is built to take into account atmospheric stability.