# Computing Kolmogorov/Energy spectrum for turbulent boundary layer

Previously, I have calculated energy spectrum for 3D DNS data obtained for isotropic turbulence which is equally spaced in all three directions and then to compute the energy spectrum, one performs Fourier transform and then accumulates energy located in different wavenumber bins and then gets the ($k^{-5/3}$) slope and it all works fine.

Now if I want to extend the same for a turbulent boundary layer case, how should I modify the technique? I cannot take a Fourier transform in the wall normal direction anymore and I am not sure how to compute the energy spectrum as such. There is no problem if I compute the spectrum for streamwise and spanwise plane since they are both defined using Fourier basis.

So my question is two-fold:

1. How do we compute energy spectrum for a 3D turbulent boundary layer?
2. If we cannot compute it for a 3D case i.e. if the argument is valid only for a 2D planar cut at various wall normal locations, then how do we define a scale for turbulent boundary layer cases, particularly along wall normal direction?

1) One usually chooses one or two representative wall-normal distances and presents the spectra for <u'u'>, <v'v'>, etc. over the homogeneous directions. For example, see Figure 11 within Spalart 1988 (http://dx.doi.org/10.1017/s0022112088000345).