If the mass of air at the top of the tower is cooled by water evaporation I could see it moving down. Depends on the temperature and density gradients inside and out. Plenty of ways to get the water to the top of the tower at little energy cost. My only question is why? There are dozens of other energy capture technologies that are more efficient. Solar, wind, geothermal, hydro, artificial geothermal (injecting water into deep dry wells which are hot at depth to produce steam) and my favorites, the thorium reactor and thorium battery. We could go farther off the reservation and talk about LENR and zero point energy capture, but that's a ways down the road.
