On the spread and decay of wind turbine wakes in ambient turbulence

The decay of the downstream wake of a wind turbine plays an important role in the performance of wind farms. The spread and decay of a wake depend both on wake meandering (advection of the wake as a whole) and wake diffusion (widening of the wake within its meandering frame of reference). Both of these effects depend strongly on the intensity of the ambient turbulence relative to the velocity deficit in the wake, and on the integral length scale of the turbulence relative to the wake width. Recent theory, which we review here, shows how intense large-scale turbulence can lead to a rapid x(-2) decay in the time-averaged centreline velocity deficit, as compared to a x(-1) decay for smaller scale turbulence, where x is distance downstream. We emphasise in this paper that common wind farm models do not predict this rapid decay. We present new experimental measurements of the velocity deficit downstream of a porous disc in relatively large-scale ambient turbulence which corroborate predictions of a x(-2) decay, and we show theoretically that the commonly used k-epsilon model does not capture this effect. We further show that a commercial CFD package, configured to match our experiments and employing the k-c model, fails to predict such rapid decay. We conclude that steady simulations of wind turbine wake dynamics are insufficient for informing wind farm layout optimisation.