But isn't the idea that you would end the column well before the air in it reaches equilibrium, and that way you would have a major temperature pressure gradient from the exit into the surrounding atmosphere, which would create a continuous flow?
Sure you would want to, but there aren't any solutions to the equations where those conditions are met.
Think if it in terms of energy in versus energy out. Where does the energy come from? Well the author is attempting to use the latent heat in the air. So you have to ask how much energy is there? You can start with Carnot and his principles of heat engines, but you also have to consider the ideal gas law, the temperature of the air goes down with a decrease in pressure. How much? Well if you look at the typical math the loss in temperature from the decrease in pressure between the top and the bottom of the chimney is exactly equal to the temperature difference measured at the top and bottom of the chimney. That situation is true because there is no net input of energy to raise the temperature of the air. So this relationship holds from altitude 0 to the bottom of the stratosphere. At the start of the stratosphere the atmosphere gets hotter as you go up[1].
Solar energy due to ground warming is contributed evenly for a first approximation across solid ground (note that cities are hotter than vegetation etc). There is no way to 'preferentially capture' just the warm air at the base of the chimney (see Maxwell's Demon[2])
At the end of the day, there is no "excess energy" to harvest there.
[1] "Within the stratosphere temperatures increase with altitude (see temperature inversion); the top of the stratosphere has a temperature of about 270 K (−3°C or 26.6°F).[5] This vertical stratification, with warmer layers above and cooler layers below, makes the stratosphere dynamically stable: there is no regular convection and associated turbulence in this part of the atmosphere." -- https://en.wikipedia.org/wiki/Stratosphere
That doesn't quite add up to me. After all, we extract energy from heating differentials all the time in the form of windmills. This really just seems like a scheme for channeling what is basically the same air circulation. The argument being that ground-warmed air doesn't typically rise in a straight line, and so by preventing lateral convection, you'll get a much faster flow up the chimney.
The use of it for wind energy is less interesting to me, though, than the idea of getting hot air radiating further from the surface of the Earth. If that is indeed significant in how the greenhouse effect works, that alone seems worth considering.
My layman's understanding is that wind is caused by pressure differences that result from different regions on the ground heating up differently in the sun. But the pressure difference between the ground and air higher up is just right to balance out gravity, so on average you should expect no movement at all.
Additionally, windmills work without any kind of tunnel, so you should expect this tower to work just as well if you just pointed a few wind turbines downward on a pole. But I think the horizontal winds would be much stronger, so you should readjust the direction a bit, which leaves you with a really tall windmill.
My understanding is that this balancing out with gravity would be true, but for horizontal mixing that occurs, as well as downdrafts of cold air and radiation (which is significant enough to motivate the chimney idea, according to the author). So you have this very complex voyage of ground-heated air upward, which is responsible for most of what we think of as local weather.
I understand the idea is to streamline the updraft, essentially controlling weather in the immediate vicinity.
