At a Glance:

Winds on Earth are a result of the sun warming the tropics more than the poles.  Like a steam engine, the atmosphere converts the thermal energy of the sun into the kinetic energy of the moving winds.  Weather models tell us that the exact pattern of the winds is sensitive to surface roughness (trees, waves on the ocean, and the like), but to make a significant effect the changes need to cover significant regions of the Earth.  

A Deeper Dive:

The winds are always exerting stresses on land and ocean–that’s where wind erosion and the energy of ocean currents comes from!  We can consider the potential impacts of wind farms on the atmosphere in a number of different ways.

Let’s consider whether the wind farms could extract enough energy to affect the winds overall (including the major patterns like the Jet Streams and Hadley Cells).  Jacobsen and Archer (2012: https://gmd.copernicus.org/articles/8/1339/2015/) studied this exact question, and found that extracting half of the world’s energy needs (5.75 TeraWatts) from the winds would have only a small impact.  It’s not until > 250 TeraWatts are extracted does the extraction significantly change the atmospheric patterns. That’s if we were generating over twenty times current energy needs for the whole of humanity from wind alone.  

Now, let’s think instead about increasing the roughness of the ocean surface with turbines.  Roughness is a measure of how bumpy the lower atmosphere finds the surface–trees and cities are bumpy, flat oceans and cornfields less so.  A simple way to understand how a farm of turbines may affect the atmosphere is to increase the roughness locally. Molod and company (2015: https://gmd.copernicus.org/articles/8/1339/2015/) did an experiment closely related to the roughness of the ocean in order to improve NASA’s weather model (called MERRA) from version 1 to version 2.  They find that they get better predictions of weather patterns when they increased the assumed roughness of the ocean by roughly double for mid- to high-wind speeds.  From our perspective, the important thing is that MERRA version 1 was a pretty good model, and so it had reasonable weather patterns, and MERRA2 is slightly better.  So, substantial changes to the surface roughness globally do not affect the overall weather patterns, much less regional changes where it is convenient or planned to build offshore wind farms.

Finally, wind turbines do disrupt the flow of air and lead to stronger mixing of the lower atmosphere.  Miller and Keith (2018: https://doi.org/10.1016/j.joule.2018.09.009) studied this effect in a model, and found that if the entire electricity demand of the US were met by wind farms it would lead to warming of the continental US by about 0.24 degrees C.  That is a lot, but much less than the 3 to 5 degrees C expected by the end of the 21st century if we do not reduce emissions by fossil fuels! (One tenth as much.) Another study (https://dx.doi.org/10.1088/1748-9326/aaea0b) found a similar magnitude of effect in observations and simulations of an offshore wind farm wake.  Again, the key idea is that the turbines enhance mixing of the lower atmosphere and bring down warmer air aloft toward the surface.