Open AccessModeling probability density functions of velocity fluctuations in wind farms
Author(s) -
Kreienkamp Kim L.,
Wilczek Michael
Publication year - 2022
Publication title -
wind energy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.743
H-Index - 92
eISSN - 1099-1824
pISSN - 1095-4244
DOI - 10.1002/we.2707
Subject(s) - statistical physics , advection , probability density function , turbulence , decorrelation , physics , superposition principle , wind speed , mechanics , stochastic process , flow (mathematics) , meteorology , mathematics , classical mechanics , statistics , quantum mechanics , thermodynamics
Summary The 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.