How do I save power spectra at different y locations ?

emmanuel germaine, 2009-01-29 12:10

I want to plot the 1D energy spectra (Euu=f(kappa)) at different y-location (e.g, one close to the wall and the other close to the centerline).

Can I do that starting with the following ?

  u.makeSpectral();
  u.saveSpectrum("data/uspectra");

Thank you Emmanuel

Discussion

John F. Gibson, 2009-02-08 07:59

Ooops! I haven't been checking this forum often enough.

No, the FlowField::saveSpectrum function saves a 2D function E(kx,kz) where

Latex

I.e the (square root of) the total energy in the kx,kz Fourier mode.

Can you write n expression for me the quantity you want to compute in terms of the velocity field? Then I can tel you how to compute it.

John

John F. Gibson, 2009-02-10 07:34

I mean, write down an expression that shows mathematically how the quantity you are interested is derived from the velocity field. E.g. for vorticity, it would be

$Graph$

There are too many conventional quantities in fluid mechanics for me to keep track of!

John F. Gibson, 2009-02-12 19:37

Gotcha. There is not a built-in function for doing this but you could write one along these lines


array<Real> Ekx(FlowField& u, int ny) {
  u.makeState(Spectral, Physical);
  array<Real> rtn(u.kxMax());
  for (int kx=0; kx<u.kxMax(); ++kx) {
    Real sum=0;
    int mx = u.mx(kx);
    for (int i=0; i<u.Nd(); ++i) 
      for (int mz=0; mz<u.Mz; ++mz) 
        sum += abs2(u.cmplx(mx,ny,mz,i));
    rtn[kx] = sum;
  }
  return rtn;
}

and similarly for kz. A couple caveats: The textbook E(kappa_x) is for continuous kappa_x and the above is for discrete values kx, where kappa_x = 2*pi*kx/Lx. You would have to double-check that relation and test out the results on some known functions to be sure. Also, the above code only produces E(kx) for kx>0. I suppose it'll be symmetric in +/- kx for real-valued fields, right?

John