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!!
Dear Alberto,
Thank you very much for your comment. Indeed I tried using the IFFT but the solution was not right. Becuase I started with an Energy Spectrum which a turbulent kinetic energy of 0.5 (The integral over the wavenumbers). Thus the velocity field I got was pretty far from it. Also I defined the man as zero. This assumption may leads to a velocity field which the maximum value cannot be greater than 1.
The phases are known because, the energy spectrum goes from k=0 to k=pi/dx (Nyquist). So in theory is possible; but maybe I messed it up in the process.
By the way, I only want the initial velocity field, not the time series!!!
Thanks
Julio
Hi Alberto, I fully agree with you. indeed I also thought about the same issue and your statement re-confirm it.
Your explanation was very elaborated, thank you very much!!
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