BUG: Inconsistent energy spectrum with boxTurb (#1804) · Issues · Development / openfoam

BUG: Inconsistent energy spectrum with boxTurb

The utility boxTurb is supposed to generate a divergence-free velocity field with the following energy spectrum

E(\kappa) = A_0 (\frac{\kappa}{\kappa_0})^4 e^{-2 (\frac{\kappa}{\kappa_0})^2}

However, when analyzing the energy spectrum from the file graphs/0/Ek.xy which appears appear running the application boxTurb, I don't see at the expected spectrum from the previous equation. I attach a picture comparing the obtained spectrum vs the theoretical spectrum.
The computation of the ensemble kinetic energy presents a multiplication by a factor for 3 which seems wrong for me as k = \int_0^{\infty} E(\kappa) d\kappa = average(\sum \frac{1}{2} mag(U)^2) = \frac{3}{2} u_{RMS}^2

Info<< "k("
         << runTime.timeName()
         << ") = "
         << 3.0/2.0*average(magSqr(U)).value() << endl;

At last the values of the wavenumber output in graphs/0/Ek.xy seems to not be in accordance with the mesh. One expects the maximum wavenumber to be \kappa_{max}= \frac{\pi}{h} where h is the cell size but I in my tests the maximum value of the wavenumber is not consistent with the theoretical formula

Run boxTurb in the boxTurb16 tutorial increasing the number of cells in each direction to 64 and changing the scale parameter to scale 6.28318530718; This value corresponds to 2pi. Decaying isotropic turbulence are commonly simulated using a box with 2pi edge length
Compare the data from the file graphs/0/Ek.xy with the theoretical spectrum from the previous equation