BUG: Inconsistent energy spectrum with boxTurb

Summary

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}

1. 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.

2. 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;

3. 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

Steps to reproduce

1. 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
2. Compare the data from the file graphs/0/Ek.xy with the theoretical spectrum from the previous equation

Example case

What is the current bug behaviour?

What is the expected correct behavior?

Relevant logs and/or images

Environment information

• OpenFOAM version : v2006
• Operating system : ubuntu
• Hardware info : -
• Compiler : -

Possible fixes

changed the description

changed the description

assigned to @kuti

changed milestone to %v2012

changed title from Inconsisten energy spectrum with boxTurb to Inconsistent energy spectrum with boxTurb

changed the description

Dear @ssss, thanks for raising the issue.

Could you suggest a fix, if possible?

changed milestone to %v2112

added bug label

changed title from Inconsistent energy spectrum with boxTurb to BUG: Inconsistent energy spectrum with boxTurb

changed milestone to %v2206