Breakdown of the velocity and turbulence in the wake of a wind turbine – Part 1: Large-eddy-simulation study

Abstract

A new theoretical framework, based on an analysis in the moving and fixed frames of reference (MFOR and FFOR), is proposed to break down the velocity and turbulence fields in the wake of a wind turbine. This approach adds theoretical support to models based on the dynamic wake meandering (DWM) and opens the way for a fully analytical and physically based model of the wake that takes meandering and atmospheric stability into account, which is developed in the companion paper. The mean velocity and turbulence in the FFOR are broken down into different terms, which are functions of the velocity and turbulence in the MFOR. These terms can be regrouped as pure terms and cross terms. In the DWM, the former group is modelled, and the latter is implicitly neglected. The shape and relative importance of the different terms are estimated with the large-eddy-simulation solver Meso-NH coupled with an actuator line method. A single wind turbine wake is simulated on flat terrain, under three cases of stability: neutral, unstable and stable. In the velocity breakdown, the cross term is found to be relatively low. It is not the case for the turbulence breakdown equation where even though the cross terms are overall of lesser magnitude than the pure terms, they redistribute the turbulence and induce a non-negligible asymmetry. These findings underline the limitations of models that assume a steady velocity in the MFOR, such as the DWM or the model developed in the companion paper. It is also found that as atmospheric stability increases, the pure turbulence contribution becomes relatively larger and pure meandering relatively smaller.