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.

 

[astrokreng]

Wavenumber is a measure of the spatial frequency of a wave, defined as the number of complete wave cycles per unit distance. In the context of turbulence, wavenumber is used to describe the size of the eddies or vortices that are present in the flow. These eddies are responsible for the dissipation of energy in the turbulent flow.

In the ocean, turbulence can be caused by various factors such as wind, tides, and density differences in the water. As the water moves, it creates eddies of different sizes, from large-scale eddies that span several kilometers to small-scale eddies that are only a few centimeters in size. The energy of these eddies is dissipated through processes such as friction and viscosity.

By using wavenumber, scientists can quantify the different sizes of eddies present in the turbulent flow. This is important because the energy dissipation rate is directly related to the size of the eddies. Larger eddies have a higher energy dissipation rate, while smaller eddies have a lower energy dissipation rate.

Furthermore, wavenumber can also be used to study the energy spectrum of turbulence. The energy spectrum describes how much energy is present at different wavenumbers. In turbulent flows, the energy spectrum follows a power law, with larger eddies having more energy than smaller eddies. This information can help us understand the dynamics of turbulence and how energy is transferred between different scales.

In summary, wavenumber is a valuable tool for studying turbulence and energy dissipation in the ocean. By quantifying the size of eddies and their energy spectrum, we can gain a better understanding of the processes that govern turbulent flows and their impact on the ocean environment.