Modeling probability density functions of velocity fluctuations in wind farms

Abstract

SummaryThe flow in large wind farms is a complex multiscale phenomenon, making comprehensive analytical or computational studies of velocity fluctuations challenging. Motivated by the need for simple, physics‐based analytical approaches to short‐time wind velocity prediction, we derive a statistical model for the spatio‐temporal evolution of streamwise velocity fluctuations in wind farms. Here, we show that the one‐point—one‐time probability density function of velocity fluctuations can be modeled by a weighted superposition of two Ornstein‐Uhlenbeck processes. The model is extended to a one‐particle advection model assuming Taylor's hypothesis of frozen turbulence. We find that our advection model captures the decorrelation process of streamwise velocity fluctuations observed in experiments.