[juliom]

Dear Community, I would like to know if you have tried to map the energy spectrum with its associated velocity field. Imagine that I have the energy spectrum at t=0; E_K(k,t=0)=f(k) where k is the wavenumber.
When we compute the energy spectrum we basically computed the FFT of the velocity (assuming 1D) and the multiply each component by its conjugate and we get the Energy Spectrum. However, during this operation, we lost the connection between the mesh and the wavenumber because we only have half of the wavelengths. This is due to the fact that the FFT goes from N/2-1:k:N/2 or usually we write K=0:N/2 - 1. So that the maximum wavenumber matches with the Nyquist wavenumber.
So, how can we do the inverse process?? I have tried but my solution is meaningless.
Thanks beforehand!!