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hao June 30, 2008 08:55

evaporation of water cause vortex?
Does water evaporation cause formation of vortex above the water-air interface? Someone knows about that?

Patrick June 30, 2008 11:15

Re: evaporation of water cause vortex?
Well, how shall I put it ? There is a very obvious weather pattern doing this: huricanne (cyclone, typhoon).

The air above the Sahara desert is heated up and as the winds are moving this hot air to the west over the ocean, the water there evaporates, a low pressure system forms. As the pressure is low locally, the air that is around moves inward to fill in the low pressure as the humid air in the middle goes up.

Now the rotational velocity of the earth is faster at the equator than at the North/South poles (since the radius of rotation goes to zero at the poles). The earth rotates to the East. Therefore when winds are moving from the equator to the North, they have a large speed easterward and they are deflected to the east. WInds moving from the north pole toward the equator have a smaller speed eastward and will be deflected to the West. So when two winds, one coming from the north and one coming from the equator are meeting (as in the case of that low pressure system), the winds coming from the equator are deflected east while the winds coming from the north pole are deflected west. These winds are like two giant hand and they actually "roll" air between them (like you can roll your pencils between your hands by moving them in opposite direction). This huge rolling of air create a gigantic vortex which can get stronger as more water evaporates as it crosses the ocean leaving the coast of Africa and reaching the east coast of the Americas.

The whole earth amosphere is a two dimensional flow (as the thickness of the atmospheric layer is very thin compared to the surface of the planet) and in two-dimensional flow there is an inverse cascade of energy which makes little vortices grow into a larger one. In short because of that the vortex that formed into a hurricane is a coherent structure that is long-lived and does not dissipate quickly.

So that is how a two dimensional vortex can form, same for the great red spot on the planet Jupiter.

Now in order to form a vortex you need to have this on a large scale. Water evaporating above a lake won't do, you need very large surface, so that the curvature of the earth enters the picture (otherwise it just like a flat surface with no differential rotation).

Hao July 1, 2008 00:12

Re: evaporation of water cause vortex?
Thank you very much, man. Actually, i am doing a CFD simulation to model the formation of a hurricane-like vortical flow driven by evaporation on the bottom and condensation on the top. I don't think i need to do a 3D one because the vortex in the horizontal plane is primarily led by the rotation of the earth. However, my supervisor require me to give him some proof to convince him. So, would you please tell me in which books you've got such points? Thank you once again.

Patrick July 1, 2008 09:14

THere are plenty of books out there, you would just need to go and dig them out. Here are a few.

- Gill, A.E., 1982, Atmosphere-Ocean Dynamics, Academic Press, New York.

- Landau, L.D., & Lifshitz, E.M., 1987, Fluid Mechanics (translated from the Russian edition "Gidrodinamika"), New York, Pergamon Press. (that's a theory book on which you can find more info on turbulence, eddies, etc..)

- Pedlowski, J., Geophysical Fluid Dynamics, Springer, New York, 1986

see the articles of James Cho: - Cho, J.Y.K., & Polvani, L.M. 1996, Physics of Fluids, volume 8, number 6, page 1531. - Cho, J.Y.K., & Polvani, L.M. 1996, in the journal "Science", n.273, page 335.

See also the papers of Marie Farge: Fage, M., & Sadourny, R., 1989, Journal of Fluid Mechanics, volume 206, page 433.

You will need a driving mechanicsm to create the vortex, the local shear due to the earth rotation is not enough to create the vortex. In pure 2D you will need to consider compressibility and put a low pressure locally. Otherwise you can simulate more than 2D and have stratified layers (like onion shells), a few layers should be enough. See the papers by Jame Cho, these are on the simulation of the Jovian atmosphere (Jupiter).

Hao July 2, 2008 00:21

Re: books
Thank you very much, Patric. It really helps a lot. By the way, would you please recommend me some other reading materials about CFD simulation of Hurricane-like vortical flows? Once again, thanks a lot.

Tom July 2, 2008 04:58

Re: books
Try searching for papers by M. T. Montgomery and look at the Journal of Atmospheric Sciences.

Patrick July 2, 2008 09:30

I don't know too much about books, but see all what you can find by Ingersoll (at CalTech), he has plenty of papers on Jupiter's atmosphere and simulations.

Here is a link to his bibliography...

You must find there something on the Great Red Spot of Jupiter (a mega-hurricane).

You just need to search in the right places, journals, sites, etc...

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