Explanation of Wavenumber wrt Turbulence and Energy dissipation

[TAFKARS]

Hi there

Can anyone provide me with an explanation of what a wavenumber is, and how it can be used in determining the extent to which energy is dissipated during turbulence (ideally in the context of the ocean)? I am aware of the basic definition of a wavenumber (i.e. the reciprocal of wave length), but I cannot seem to make this next mental leap!

Many thanks...

 

[Andy Resnick]

I've heard of this idea, I think first put forward by Leo Kadanoff. "Energy cascades" are invoked to describe dissipative processes, of which turbulence is one, whereby large coherent structures evolve into smaller structures with lower mutual coherence. Viewed in reciprocal space (via the Fourier transform), the characteristic wavenumber of the excitation increases over time.

If you like, the coherence length of excitations in a dissipative system decreases over time. In terms of water waves, a large initial disturbance decays into smaller waves, with the smalelr waves becoming more and more incoherent with each other. A large vortex will decay and dissipate (leading to a natural question regarding the stabiltiy of Jupiter's great red spot).

That's about all I know. It's an interesting concept, and I should know more about it.