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 Tae-Chang Jo September 16, 1999 20:57

geophysical turbulence

Can anyone explain what geophysical turbulence is? Thank you.

 Md. Ziaul Islam September 17, 1999 00:26

Re: geophysical turbulence

The study of geophysical fluid flows has taken on a new popularity, and urgency, with an increasing awareness of the complexity and delicate balance of the intermediate and large scale motions of the fluids in which all life on earth occurs. The physical problems typically involve an interaction between the usual equations of motion for a homgeneous fluid, together with additional contstraints arising from the planetary rotation, or density stratification. Motion at interfaces between fluids of different densities can give rise to linear and nonlinear waves, and the interaction between waves and turbulence is also arecurrent theme. Hurricane is a good example of geophysical turbulence. The acceleration caused by the rotation of the earth is much larger than that due to the translation of the earth's center. Coriolis acceleration plays an important role for the hurricanes to rotate as well as move the way we can see when we try to visualize satellite pictures. Let me give you a simple example of Coriolis component of the energy equations. Everybody have seen the sprinklers rotating while scattering small drops of water for watering grass and flowers.

 Patrick Godon September 20, 1999 09:38

Re: geophysical turbulence

Geophysics is the study of the earth (geo) as related to its physical processes.

The main picture I have in mind of geophysical turbulence is the turbulence in the atmosphere and the waves in the sea. Both can be approximated by a 2 dimensional flow on the surface of a sphere (of infinitely small thickness h). One then solves for the velocities on the sphere and the thickness h (shallow water equations - SWE). Another way is to solve just for the velocities (vorticity equation; simpler approach). The SWE has for solutions waves known as surface gravity waves, simply the waves that you can observe on the surface of the water when you drop a penny in a pool. There are also more complicated waves known as Rossby waves, associated with the rotation of the earth. For the earth the main result for the atmosphere is the Jet Stream, which is a permanent feature of the earth atmosphere; these are high altitude strong winds. For different planets with different rotation velocities and different radius and gravity, there are other solutions: several jet streams (giant planets), and just a few large vortices, etc.. For example Jupiter's atmosphere has bands associated with these Jets. Another feature of Jupiter is the Great Red Spot, a huge vortex. The similarity to that kind of vortex on earth are the cyclonic vortex known in the US as huricane (typhoon). So the great red spot on jupiter is just a huge storm in some sens.

The main characteristics of these flows is that they are mainly two-dimensional (2D), on the surface of a sphere and the sphere is rotating. Because of the 2D the energy is transfered from the small scales to the large scales (inverse cascade of energy) and this is observed in the flow by the merging of small vortices to form larger vortices. Eventually only one large vortex can dominate the flow (Jupiter). Because of the rotation, Coriolis effects are important.

When strong winds pass over a mountain in certain cases they can even cause a turbulent pattern known as Von Karman vortex street, a street of vortices.. This is another kind of turbulence that can formed, not really related to the above turbulence.

For example see:

Cho and Polvani, 1996, Science 273, p. 335

And the main one is the famous book:

Peklosky,J., Geophysical Fluid Dynamics, Springer Verlag, Berlin, 1987 (second Edition).

Cushman-Roisin, and Tang 1990, J. PHys. Ocean vol. 20, p.97.

I hope this helps,

Patrick

 Patrick Godon September 20, 1999 09:43

missprint

Sorry for the missprint, the book is

Pedlosky (not Peklosky).

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