[rdemyan]

Originally Posted by FMDenaro

Some observations:
1) the inertial range in the energy spectra is also more extended than I expected. Note that the slope -5/3 in the dissipation range has no meaning as term of comparison.


2) The model dissipation spectra in Pope shows a clear exponential decay, your figure seems different, that should be the effect of the too low Re number.


3) You wrote you are working on a decadying turbulence, that means you do not have an energy equilibrium state. Energy and dissipation spectra will change during the decaying.

For the following equation for the energy spectrum:




I am confused about how the distribution of eddy sizes (independent of the energy they contain) is included in this equation. Does the eqn only include the total energy of eddies of a particular size without knowing how many of these eddies there are relative to the the total number of eddies? Or is the size distribution inherently included in the equation?

[FMDenaro]

Originally Posted by rdemyan

For the following equation for the energy spectrum:




I am confused about how the distribution of eddy sizes (independent of the energy they contain) is included in this equation. Does the eqn only include the total energy of eddies of a particular size without knowing how many of these eddies there are relative to the the total number of eddies? Or is the size distribution inherently included in the equation?

an element has the dimension l^-1. That means that while integrating along the spatial frequencies you are evaluating the contribution of energy due the whole range of eddies.

[rdemyan]

Originally Posted by FMDenaro

an element has the dimension l^-1. That means that while integrating along the spatial frequencies you are evaluating the contribution of energy due the whole range of eddies.

But would it be possible to determine the eddy size distribution?

[FMDenaro]

Originally Posted by rdemyan

But would it be possible to determine the eddy size distribution?

What do you mean exactly? The distribution is assumed to be extended up to the Kolmogorov length.

[rdemyan]

Originally Posted by FMDenaro

What do you mean exactly? The distribution is assumed to be extended up to the Kolmogorov length.

As a very hypothetical example (no doubt removed from reality) something like there twice as many eddies of size 1 as there are of size 2 which number five times as many as eddies of size 3 and so on. Something like that. Or maybe a Gaussian distribution where the number of large eddies and Kolmogorov eddies are small, but there is an eddy size somewhere in the middle where the number of those eddies is the highest.

[FMDenaro]

Originally Posted by rdemyan

As a very hypothetical example (no doubt removed from reality) something like there twice as many eddies of size 1 as there are of size 2 which number five times as many as eddies of size 3 and so on. Something like that. Or maybe a Gaussian distribution where the number of large eddies and Kolmogorov eddies are small, but there is an eddy size somewhere in the middle where the number of those eddies is the highest.

I don't know if that has some sense, you have a continuous creation, stretching, stirring and dissipation of eddies. In some problems you have also a reverse mechanism with larger structures produced by smaller one.



Note that an identification of a vortical structure is still a problem, then you should attribute also the statistical meaning of coherence to discriminate the relevant number of structures. At present, I don't remember if literature has some work with the analysis of the statistical distribution.