Including the turbulent Schmidt number in the dynamic wake meandering model

Wind turbine wakes are an important source of power losses and mechanical wear within wind farms. Wake meandering is a low-frequency oscillation of the entire wind turbine wake with respect to the time-averaged centerline. It affects power losses by contributing to the recovery of the mean velocity deficit and it affects mechanical loads by increasing the turbulence intensity. Therefore, modeling wake meandering is an important part of wind farm design. The dynamic wake meandering (DWM) model is a mid-fidelity model assuming the wake to behave like a passive scalar that is transported by large-scale turbulence (Larsen et al. 2008). Several publications have shown good overall agreement of the DWM model to observations. However, it also has been observed that using a downstream transport velocity slower than the mean wind speed leads to better agreement between predicted wake center positions and observations (e.g. Machefaux et al. 2015), which points towards short-comings of the passive scalar assumption used by the DWM model. Here, we investigate the transport behavior of wake meandering further. Using wake measurements of a Doppler LiDAR mounted on the nacelle of a utility-scale wind turbine as a reference, we found a discrepancy in the predictions of the wake center position with the DWM model: i. A better temporal agreement is reached if the downstream transport uses an advection velocity slower than the mean wind speed. ii. The wake meandering strength is overestimated when using the optimal advection velocity. We hypothesize that the explanation for this discrepancy is that the transport of momentum in a wake is less efficiently than that of scalars (Reynolds 1976). Comparing the observed wake transport with the expected transport of a true scalar, we found turbulent Schmidt numbers smaller than unity indicating a transport behavior more akin to momentum than a scalar. Further, we included the turbulent Schmidt number in the transport process of the DWM model, which did reconcile the overestimation of wake meandering strength (Figure 1).