The Ambit Stochastics Project

Wind turbine turbulence


For applications in turbulence Y models the velocity vector as a function of space and time. It seems to be enough to choose the subordination


Furthermore, the Lévy basis L is white noise in space-time. With this choice of model ingredients the second term in the above formula controls the skewness of velocity increments, and the decompostion of the velocity fields into two terms resembles the well known Reynolds decomposition into a slowly varying term (the skewness term) and a rapidly varying term (the Brownian stochastic integral).

As an application to the modeling of wind farm flows, we may model the wake behind a wind turbine by choosing a suitable non-homogeneous subordinated Lévy basis to account for the fact that the turbulence is stronger within the wake compared to the surrounding flow outside of the wake. Finer details in the correlation structure can be modelled by the kernel.