Found this paper.

Flow Adjustment Inside and Around Large Finite-Size Wind Farms

Abstract

In this study, large-eddy simulations are performed to investigate the flow inside and around large finite-size wind farms in conventionally-neutral atmospheric boundary layers. Special emphasis is placed on characterizing the different farm-induced flow regions, including the induction, entrance and development, fully-developed, exit and farm wake regions. The wind farms extend 20 km in the streamwise direction and comprise 36 wind turbine rows arranged in aligned and staggered configurations. Results show that, under weak free-atmosphere stratification (Γ=1 K/km), the flow inside and above both wind farms, and thus the turbine power, do not reach the fully-developed regime even though the farm length is two orders of magnitude larger than the boundary layer height.In that case, the wind farm induction region, affected by flow blockage, extends upwind about 0.8 km and leads to a power reduction of 1.3% and 3% at the first row of turbines for the aligned and staggered layouts, respectively. The wind farm wake leads to velocity deficits at hub height of around 3.5% at a downwind distance of 10 km for both farm layouts. Under stronger stratification (Γ=5 K/km), the vertical deflection of the subcritical flow induced by the wind farm at its entrance and exit regions triggers standing gravity waves whose effects propagate upwind. They, in turn, induce a large decelerating induction region upwind of the farm leading edge, and an accelerating exit region upwind of the trailing edge, both extending about 7 km. As a result, the turbine power output in the entrance region decreases more than 35% with respect to the weakly stratified case. It increases downwind as the flow adjusts, reaching the fully-developed regime only for the staggered layout at a distance of about 8.5 km from the farm edge. The flow acceleration in the exit region leads to an increase of the turbine power with downwind distance in that region, and a relatively fast (compared with the weakly stratified case) recovery of the farm wake, which attains its inflow hub height speed at a downwind distance of 5 km.

i.e. “wind farms” are less efficient than lone turbines and their environmental disruption can prevail for several kilometres downwind.

Those of us who remember our fluid mechanics will remember rules of thumb like 20 characteristic diameters to re-establish laminar flow after a turbulent disruption — “strictly” applicable to pipes, but nevertheless relevant to open-field flow. Spacing turbines at 20 diameters is *prima facie* the starting point for deployment to reap maximum power. Spacing is as close as 5 diameters in practice which guarantees turbulent turbine interactions, significantly reducing the efficiency of the airfoils (blades).

The simulations in the paper describe somewhat the “bow wave” produced by the wind farm obstacle; which further reduces efficiency and power output. This is predictable if one understands Le Chatelier’s Principle which can be paraphrased as *“nature finds the easiest way to do things”*. In this case; if the wind farm becomes sufficiently obstructive (corresponding to a large, nominal power output), wind would tend to go around or even over the top of the wind farm.

Lest you think that this is purely theoretical then spend some time sitting on a hill, watching how a rainstorm and clouds flow to follow the landscape.