[bhigahAshish]

Hi all,

this post can be placed here and in the the lounge as well.

It is a really frustrating period for me, my advisor thinks that the Energy spectrum is the Fourier Transform of the time history of the specific Turbulent kinetic energy.

I demonstrated that the mean value of turbulent kinetic energy is equal to the integral of the energy spectrum over the frequency, which could be a definition of the energy spectrum, as you can see at page 53 of the book "Turbulence" of Uriel Frisch, but maybe because I am young and just arrived he does not believe in what I am saying.

I also tried to do the Fourier Transform of the time history of the specific Turbulent kinetic energy and I showed him that it is not demonstrated that the mean value of turbulent kinetic energy is equal to the integral of the energy spectrum over the frequency. (He thinks that I am wrong in some scaling factor after doing the fft, which it is impossible since, using the proper definition of the Energy spectrum, this demonstration checks)

I think that that the name of this spectrum confused him, I have seen some confusion here as well Power Spectral Density - Energy Spectrum .

The problem here is scientific and psichological. I would like to do a demonstration that the Fourier Transform of the time history of the specific Turbulent kinetic energy is not the Energy spectrum, but it seems difficult to me prove this idea. I know that in this group there are expert scientists and I am searching for advices, I hope you can help me.