  We present and test the coupled wake boundary layer (CWBL) model that
describes the distribution of the power output in a wind-farm. The model
couples the traditional, industry-standard wake model approach with a
"top-down" model for the overall wind-farm boundary layer structure. This wake
model captures the effect of turbine positioning, while the "top-down" portion
of the model adds the interactions between the wind-turbine wakes and the
atmospheric boundary layer. Each portion of the model requires specification of
a parameter that is not known a-priori. For the wake model, the wake expansion
coefficient is required, while the "top-down" model requires an effective
spanwise turbine spacing within which the model's momentum balance is relevant.
The wake expansion coefficient is obtained by matching the predicted mean
velocity at the turbine from both approaches, while the effective spanwise
turbine spacing depends on turbine positioning and thus can be determined from
the wake model. Coupling of the constitutive components of the CWBL model is
achieved by iterating these parameters until convergence is reached. We
illustrate the performance of the model by applying it to both developing
wind-farms including entrance effects and to fully developed (deep-array)
conditions. Comparisons of the CWBL model predictions with results from a suite
of large eddy simulations (LES) shows that the model closely represents the
results obtained in these high-fidelity numerical simulations. A comparison
with measured power degradation at the Horns Rev and Nysted wind-farms shows
that the model can also be successfully applied to real wind-farms.
