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Skyscrapers sway in the wind (Source here). Which direction, relative to the wind, do they sway, ignoring effects of other buildings nearby?

I can imagine wind from the North blowing a skyscraper's tip to the South, and then (because wind isn't a constant velocity) the tip swaying back towards center. With the right changes in velocity you could get some noticeable resonance, perhaps.

I could also imagine wind from the North causing resonant vortex shedding on the downwind side, inducing an East/West component to the motion. I sort-of suspect that this would be a more significant factor, and that most motion would be in this transverse direction, but I'm not sure how it'd be calculated or shown.

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It depends mostly on the shape of the building.

For example, imagine a skyscraper that's got the aspect ratio like a stick of gum: maybe 400 meters vertical height, 90 meters north-south, and only 30 meters east-west. Such a building, no matter how it is reinforced internally, is going to oscillate in an east-west direction much more readily than in the north-south direction. It's just easier for the building to bend the skinny way rather than the wide way.

A more traditionally-shaped skyscraper with a square-ish cross section might be better able to oscillate along either axis. However, in that case, the internal structures in the building will tend to mix the north-south and east-west oscillation modes, in a way that may or may not involve a torsion mode where the building twists. Figuring out how the energy of these oscillations is dissipated, whether the energy is delivered from the wind or from seismic oscillations in the ground, is an important and complex part of designing sturdy buildings.

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