The interplay between helicity and rotation in turbulence: implications for scaling laws and small-scale dynamics

Abstract

Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of helicity conservation (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, with solid body rotation, significant differences emerge between helical and non-helical flows. We first outline several results, like the energy and helicity spectral distribution and the breaking of strict universality for the individual spectra. Using massive numerical simulations, we then show that small-scale structures and their intermittency properties differ according to whether helicity is present or not, in particular with respect to the emergence of Beltrami-core vortices (BCV) that are laminar helical vertical updrafts. These results point to the discovery of a small parameter besides the Rossby number; this could relate the problem of rotating helical turbulence to that of critical phenomena, through renormalization group and weak turbulence theory. This parameter can be associated with the adimensionalized ratio of the energy to helicity flux to small scales, the three-dimensional energy cascade being weak and self-similar.