Helicity scalings

Abstract

Using a helical shell model of turbulence, Chen et al. (2003) showed that both helicity and energy dissipate at the Kolmogorov scale, independently from any helicity input. This is in contradiction with a previous paper by Ditlevsen & Giuliani (2001) in which, using a GOY shell model of turbulence, they found that helicity dissipates at a scale larger than the Kolmogorov scale, and does depend on the helicity input. In a recent paper by Lessinnes et al. (2011), we showed that this discrepancy is due to the fact that in the GOY shell model only one helical mode (+ or -) is present at each scale instead of both modes in the helical shell model. Then, using the GOY model, the near cancellation of the helicity flux between the + and - modes cannot occur at small scales, as it should be in true turbulence. We review the main results with a focus on the numerical procedure needed to obtain accurate statistics.