There seems to be a problem with estimates of the total amount of energy available for harvesting from the wind.  Most calculations assume that  extracting  wind energy doesn't alter large-scale winds enough to significantly limit wind power production.

But that's wrong, say researchers from the University of North Carolina at Charlotte and  Harvard University, who wrote up their conclusions in a recent issue of the journal Environmental Research Letters. The problem, they say, is that you can't  ignore the effect of wind turbine drag on local winds when making such estimates. A mathematical model they've devised that takes such effects into consideration suggest that wind power production is limited to about 1 W/m2 at wind farms larger than about 100 km2. That's only about 25% of some estimates of worldwide wind power resources.

 The researchers, Amanda Adams and David Keith, arrive at their conclusions by first considering how surface winds originate. Most of the kinetic energy that drives surface winds originates from factors such as the difference in temperatures between the poles and the equator. When wind turbines operate at a relatively low capacity factor -- meaning they harvest wind energy a low percentage of time -- the effect on the remaining wind energy can be neglected, the researchers say. Then the power density produced by a given wind farm will increase linearly with the turbine density. However, as you pack more turbines into a given area, winds must slow and the capacity factor must decline so power density grows at a rate that is less than linear. At a sufficiently high turbine density, the power produced reaches a maximum and then drops as the rising turbine density slows the winds.

The two researchers used a model based on observed velocity- dependant drag coefficients of wind turbines but not down to a point where it considers individual turbines. Basically the researchers divided land area into a grid box and defined a wind turbine density for each grid box that represents the area swept by the turbines per grid box volume. They say the wind turbine density takes into account both the horizontal density of the wind turbines as well as the fraction of the turbine blade that is in a grid box vertically.

Modeled this way, a wind farm with a capacity density of 4 W/m2 shows a drop in wind speed of about 40%. The researchers say their results suggest that power production as a function of rising turbine density begins to saturate below 1 W/m2 and that it will be difficult to attain large-scale wind power production with a power density of much greater than  2 W/m2. This contradicts the assumptions in common estimates of global wind power capacity, they say.

The researchers summarized their findings in a YouTube video.