"There is no air at a point. A point, by definition, has no volume. Are you manufacturing air?"
Sorry. Assume an area, heat it up and wind flows out of it. However the air in the area itself is moving, so conceptually all the air is moving out of the point in the center of it. (It's not really, it's moving out of the area, but all the vectors point away from the point, so that's what it looks like.)
"It's true that the theorem does not require a cyclone."
Thanks. That's really all I was arguing about.
The thing with continuous and cyclone: I was assuming, that people were saying, that the wind _always_ has to move - even if in a circle. And I was saying, no, it doesn't have to move, you can have a still area, and wind radiating out of it (or into it).
If I am correct about that, then please edit the wikipedia article to remove mention of cyclones.
Why do you say that can't happen in a 2d fluid flow? Why does it have to be a cyclone? My understanding of weather is you have a large area, you heat it up, and wind flows out of it - but there is no cyclone. (I guess with fluid flow you are assuming there is no way to manufacture fluid, but with wind you can since heat will "create" more of it.)
Tell me if I'm wrong here:
The hairy ball theorem assumes there is hair everywhere, so you have to have a cyclone at the poles. But with wind there are spots without hair, so the theorem just doesn't apply to wind.
Sorry. Assume an area, heat it up and wind flows out of it. However the air in the area itself is moving, so conceptually all the air is moving out of the point in the center of it. (It's not really, it's moving out of the area, but all the vectors point away from the point, so that's what it looks like.)
"It's true that the theorem does not require a cyclone."
Thanks. That's really all I was arguing about.
The thing with continuous and cyclone: I was assuming, that people were saying, that the wind _always_ has to move - even if in a circle. And I was saying, no, it doesn't have to move, you can have a still area, and wind radiating out of it (or into it).
If I am correct about that, then please edit the wikipedia article to remove mention of cyclones.
Why do you say that can't happen in a 2d fluid flow? Why does it have to be a cyclone? My understanding of weather is you have a large area, you heat it up, and wind flows out of it - but there is no cyclone. (I guess with fluid flow you are assuming there is no way to manufacture fluid, but with wind you can since heat will "create" more of it.)
Tell me if I'm wrong here:
The hairy ball theorem assumes there is hair everywhere, so you have to have a cyclone at the poles. But with wind there are spots without hair, so the theorem just doesn't apply to wind.