Idea of exercice with ns3d: spectra in non-stationnary decaying turbulence
It would be interesting to investigate numerically ideas described here: https://meetings.aps.org/Meeting/DFD21/Session/P04.4
For the decaying turbulence, one can use phase shifting time stepping.
We can also look at what it gives with a wake of a sphere (forcing in physical space with a kind of "laminarisation region").