Here, we build a model
describing the essential features of a large array of turbines with arbitrary design and layout,
by considering a fully-developed wind farm whose upper edge is bounded by a self-similar
boundary layer. The exchanges between the wind farm, the overlaying boundary layer, and
the outer flow are parametrized by means of the classical entrainment hypothesis.We obtain
a concise expression for the wind farm’s power density (corresponding to power output per
unit planform area), as a function of three coefficients, which represent the array thrust
and the turbulent exchanges at each of the two interfaces.
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