Understanding turbulence through numerical simulations

Turbulence is one of the important problems in classical physics that still remain unsolved. The Navier–Stokes equations have been studied for almost two centuries now, and although they seem to properly describe the dynamics of fluids, we still do not have a clear understanding of even the simplest turbulent flows. We present numerical simulations of three dimensional, homogeneous and isotropic turbulence at moderate Reynolds numbers. We externally drive the fluid with either helical or non-helical forces. In both cases we find that the externally driven system relaxes to a stationary turbulent regime, which is compatible with the Kolmogorov spectrum Ek≈k−5/3. In the helical case, we confirm that the kinetic helicity also cascades directly, along with energy and displaying a Kolmogorov spectrum as well. We find that the dissipation scale of both ideal invariants is also consistent with the Kolmogorov scale (i.e., kν≈( /ν3)1/4).