Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Abstract

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small-scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.

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• Dynamic Phase Alignment in Inertial Alfven Turbulence
• Pseudo-invariants causing inverse energy cascades in three-dimensional turbulence
• A closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence
• Dynamic Phase Alignment in Navier-Stokes Turbulence
• Partial invariants, large-scale dynamo action, and the inverse transfer of magnetic helicity
• A self-induced mechanism of large-scale helical structures in compressible turbulent flows