Modeling space-time correlations of velocity fluctuations in wind farms

TL;DR

This paper introduces an analytical model based on the Kraichnan-Tennekes hypothesis to predict the space-time correlations of velocity fluctuations in wind farms, validated against large eddy simulation data.

Contribution

The paper develops a novel analytical model linking spatial correlations to temporal decorrelation in wind farm turbulence, validated with LES data.

Findings

Model accurately predicts space-time correlations in wind farm turbulence.

Spatial correlations can be used to infer temporal fluctuation structures.

Good agreement between model predictions and LES data.

Abstract

An analytical model for the streamwise velocity space-time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space-time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatio-temporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatio-temporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full temporal structure of fluctuations in wind farms.