7 ms·
Does the hairy ball theorem imply that there is always some place on the earth's surface where wind speed is zero?
by siddboots 13y ago
Does the hairy ball theorem imply that there is always some place on the earth's surface where wind speed is zero?
- jackmaney 13y agoYes, assuming that the wind vectors are orthogonal to the Earth (and that the Earth is spherical). Also, by the Borsak-Ulam Theorem ( http://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem http://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem ), there are two points on the Earth directly opposite one another that have the same wind speed.
- nilkn 13y agoI think slight disturbances from being perfectly spherical are fine (since the Euler characteristic wouldn't be affected). The wind vectors not always being orthogonal to the Earth seems more damning, but maybe it is enough to just consider their projection onto the Earth's surface.
- 3rd3 13y agoIs it a problem that air can change in density/that it can be compressed?