Understanding turbulence through numerical simulations

Abstract

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 6uids, we still do not have a clear understanding of eventhe simplest turbulent 6ows. We present numerical simulations of three dimensional, homogeneous and isotropic turbulence at moderate Reynolds numbers. We externally drive the 6uid with either helical or non-helical forces. In both cases we ;nd that the externally driven system relaxes to a stationary turbulent regime, which is compatible with the Kolmogorov spectrum Ek ≈ k−5=3 . Inthe helical case, we con;rm that the kinetic helicity also cascades directly, along with energy and displaying a Kolmogorov spectrum as well. We ;nd that the dissipation scale of both ideal invariants is also consistent with the Kolmogorov scale (i.e., k ≈ ( = 3 )1=4).