  Many wind farms are placed near coastal regions or in proximity of orographic
obstacles. The meso-scale gradients that develop in these zones make wind farms
operating in velocity fields that are rarely uniform. However, all existing
wake-merging methods in engineering wind-farm wake models assume a homogeneous
background velocity field in and around the farm, relying on a single
wind-speed value usually measured several hundreds of meters upstream of the
first row of turbines. In this study, we derive a new momentum-conserving
wake-merging method capable of superimposing the waked flow on a heterogeneous
background velocity field. We couple the proposed wake-merging method with four
different wake models, i.e. the Gaussian, super-Gaussian, double-Gaussian and
Ishihara model, and we test its performance against LES data, dual-Doppler
radar measurements and SCADA data from the Horns Rev, London Array, and
Westermost Rough farm. Next to this, as an additional point of reference, the
standard Jensen model with quadratic superposition is also included. Results
show that the new method performs similarly to linear superposition of velocity
deficits in homogeneous conditions but it shows better performance when a
spatially varying background velocity is used. The most accurate estimates are
obtained when the wake-merging method is coupled with the double-Gaussian and
Gaussian single-wake model. The Ishihara model also shows good agreements with
observations. In contrast to this, the Jensen and super-Gaussian wake model
underestimate the farm power output for all wind speeds, wind directions and
wind farms considered in our analysis.
