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.Comment: Submitted to Wind Energ