Modeling space-time correlations of velocity fluctuations in wind farms

Abstract

An analytical model for the streamwise velocity space-time correlations in turbulent flows isderived and applied to the special case of velocity fluctuations in large wind farms. The modelis based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation intime while including a mean wind velocity in the streamwise direction. In the resulting model, thestreamwise velocity space-time correlation is expressed as a convolution of the pure space cor-relation with an analytical temporal decorrelation kernel. Hence, the spatiotemporal structureof velocity fluctuations in wind farms can be derived from the spatial correlations only. We thenexplore the applicability of the model to predict spatiotemporal correlations in turbulent flows inwind 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 andtemporal 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 thatspatial data may be used to model the full spatiotemporal structure of fluctuations in wind farms