Why does wind inside a stadium blow opposite the wind above the stadium?

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In a (American football) bowl stadium, the flags on top of the goalposts typically fly in the opposite direction of the flags above the stadium, particularly when the wind is blowing heavily. Why is that?

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Low pressure behind the windward wall and high pressure in front of the leeward wall of the stadium causes a circulatory current. Bernoulli’s principle at work.

If the air at the bottom of the stadium is moving east, then the air at the top must move west, since air can’t just vanish. That same air has to stop and turn around and go back to where it started. The result is the air at the top going opposite to the air at the bottom.

Picture a giant waterwheel. Water going over the top of the wheel falls down one way, but the opposite side of the wheel goes the other way because that’s how spinning things work. The exact same thing is happening here, except the air itself is both the water and the wheel. Wind flowing over the top of the stadium pushes the wind just below it inside the stadium along in the same direction, but then that air hits the wall of the stadium. Some of it goes up, some goes down, and the air which goes down becomes the wind flowing across field height in the stadium as it turns back around to continue spinning the wheel.

Think of an ice cream scoop. The stand roofs do kinda the same thing to the air.
Similar thing to wind blowing against a tall building, where a part of it shoots up and some of it shoots down the face of the building messing up the umbrellas on the sidewalk next to it.