# Ratio of horizontal to vertical kinetic energy in ocean

What is the ratio between horizontal and vertical kinetic energy in the ocean and what is the scale dependencies of this ratio ?

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a tag oceanography would be nice – aberration Sep 20 '12 at 22:21
Created the tag.. Thanks! – Evil Angel Dec 28 '12 at 8:44

The question is simple but the reason why it probably has not been answered yet is that the answwer is extraordinarily complex.
Basically if you consider a steady state with a velocity field V(x,y,z), you are asking to :

• find the horizontal and vertical components Vh(x,y,z) and Vv(x,y,z)

• integrate Vh².dV and Vv².dV all over the globe

This is a matter of oceanic circulation and the answers have the size of textbooks. For a more comprehensive understanding I suggest to read just 1 chapter about Ekman layer transport (http://paoc.mit.edu/labweb/notes/chap10.pdf)

Now with the caveat given, I will give you an estimate of an order of magnitude for the global integrals mentionned above.

Considering that the upwelling/downwelling cycles concern 10 % of the ocean surface and having the average depth of the oceans 3800 m this allows to estimate the mass contributing to the vertical movement. The vertical velocities of the thermohaline circulation are 1 to 0.1 mm/s depending on location. Taking the conservative value of 0.1 mm/s, this gives a "vertical" kinetic energy of 700 GJ.

The horizontal movements are slightly easier because they concern the whole surface and reach only a limited depth. However as this circulation is wind driven and the wind velocity field is highly anisotropic and chaotic, the variability is high. Considering that only the highest and lowest 100 m participate on the horizontal circulation (conveyor belt model) and that the average velocity is 0.1 m/s we obtain a kinetic energy of 300 millions GJ.

Despite large uncertainty margins due to very simplified estimations, it is clear that the "horizontal" kinetic energy is about 6 orders of magnitude higher than the "vertical" kinetic energy.

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Interesting answer. I guess that apply to the large scale part of the spectra. – aberration Jun 25 '13 at 20:23