[athos]

Hi everyone!

I am currently doing a thesis work using a Fortran-based CFD solver, and I'm at a step in which I basically have to place a set of virtual probes in some points within my fluid domain in order to collect a signal for pressure, x-velocity, y-velocity, z-velocity, temperature etc.

Disclaimer: I do not know much of spectral analysis, so sorry for the hundreds of mistakes that I am about to make, this is why I am writing a post here on this forum in order to get some help to get over this part of my thesis work

I've already placed the probes, and of course what I get is a signal in a fixed 3D point, that is, p(x0,y0,z0,t), u(x0,y0,z0,t), etc.
I have already done a little bit of post-processing on Matlab for small statistical quantities such as variance vs time, probability density function for the turbulent signal, etc, but now I would like to perform a Fourier analysis of my velocity signal in order to obtain an Energy spectrum and a Fourier analysis of my pressure too.

For now, I've only tried to do the latter: I compute my mean sampling period as the mean timestep between the measures, then Fs as 1/Ts, then the Nyquist frequency as Fs/2, and finally I use pwelch (I was told to use this and not the FFT because it automatically filters the signal) to find the PSD of the pressure signal and I plot it in logarithmic coordinates against the frequency. This is the first issue: I have to plot it against the wavenumber k, especially because all data are non-dimensional. Do I just apply the Welch's PSD and then compute the wavenumber as (2*pi*frequency)/(velocity)? And which velocity do I consider? I would say that if I want to plot a spectrum for k1 I would have to use the mean velocity in the x-direction but I am not sure at all.

The second issue is, as mentioned, how to compute the E(k1), E(k2), E(k3) spectra. I was thinking about doing the PSD of (u')^2 and then plot it against k1, and so on, but then again I'm not 100% sure on how to compute k1,k2,k3.

I want to thank everyone in advance for taking the time to read this and help me, and again sorry for the theoretical mistakes that I'm probably making for lack of competence on this specific subject.

If anyone wants to take a direct look at it, here you can find an example of a signal of one of the probes. The columns represent, from left to right, the iteration number, the time instant, the pressure, the temperature, the density, u, v, w.