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Invariance properties of physical systems govern their behavior: energyconservation in turbulence drives a wide distribution of energy among modes,observed in geophysical or astrophysical flows. In ideal hydrodynamics, therole of helicity conservation (correlation between velocity and its curl,measuring departures from mirror symmetry) remains unclear since it does notalter the energy spectrum. However, with solid body rotation, significantdifferences emerge between helical and non-helical flows. We first outlineseveral results, like the energy and helicity spectral distribution and thebreaking of strict universality for the individual spectra. Using massivenumerical simulations, we then show that small-scale structures and theirintermittency properties differ according to whether helicity is present ornot, in particular with respect to the emergence of Beltrami-core vortices(BCV) that are laminar helical vertical updrafts. These results point to thediscovery of a small parameter besides the Rossby number; this could relate theproblem of rotating helical turbulence to that of critical phenomena, throughrenormalization group and weak turbulence theory. This parameter can beassociated with the adimensionalized ratio of the energy to helicity flux tosmall scales, the three-dimensional energy cascade being weak and self-similar.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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