Comparative Analysis of the Dynamics of Wind Turbine Wakes and Passive Scalar Plumes in the Atmospheric Boundary Layer

Wind turbines are usually placed in close proximity to each other in large wind farms. A consequence of such an arrangement is that most turbines operate in the wake of one or several other turbines, rather than in unobstructed wind flow. The transient characteristics of the wakes directly determine the power losses due to the velocity deficit as well as the fatigue loads experienced by turbines operating in the wake regions. A better understanding of wake dynamics is thus crucial for developing optimal strategies towards maximizing power output and limiting fatigue loads that affect the operational lifetimes of wind turbines. One approach towards modeling the transient behavior of a wake is to treat it as a passive scalar transported by the large scale eddies in the atmospheric flow. Such analogy is used to develop analytical models that estimate the extent of wake meandering in wind farms. It is then of interest to determine the accuracy of such an approximation in predicting the dynamics of wind turbine wakes.

In this study, we perform large-eddy simulations of the advection of a passive scalar in an atmospheric boundary layer, by introducing a scalar source that is geometrically similar to a wind turbine into the flow. It is observed that the scalar plume originating from the source develops a Gaussian profile as it is transported downstream, as seen in case of a wind turbine wake. The expansion of the scalar plume as it proceeds downstream happens at a rate comparable to that of a wake for the given turbulence intensity. The transient behavior of both plume and wake is analyzed to contrast the dynamics of meandering in both cases. A good degree of correlation is observed between the instantaneous position of the wake and plume centers. At a specific downstream location, the variance of the position of the wake center is observed to be larger than that of the plume center. However, when the comparison is made instead for a specific advection time, the variance of the plume center is found to be higher than that of the wake center. Spectral analysis of the instantaneous variation of the position of wake and plume center reveals that the scales in the range of the size of rotor carry more energy in case of the plume than in the wake. Comparisons of the simulated wake and plume dynamics are also made with existing analytical models for wake meandering. The results provide insights on how to improve wake meandering models, which in turn could lead to improved design and control of wind farms.