Statistics of helicity fluctuations in homogeneous turbulence

The statistics and dynamical significance of helicity fluctuations in turbulent flows are investigated. A random-phase or quasi-Gaussian approximation (QGA) is employed to obtain expectation values of the magnitude of helicity fluctuations in reflectionally symmetric ensembles of turbulent flows. It is shown that the QGA is compatible with Kolmogorov-type scaling arguments supplemented by elementary statistical considerations. It follows from the scaling properties of the viscous term in the helicity balance equation that in the absence of phase correlations helicity is an adiabatic invariant of fully developed turbulent flows. Possible consequences of this invariance for decaying flows are discussed. In direct numerical simulations of decaying and forced turbulence it is found that at large scales the fluctuations of helicity are well described by the QGA, and as such not strong enough to directly influence the energy transfer. The helicity fluctuations at large wave numbers, on the other hand, are repeatedly observed to deviate significantly from the QGA, indicating the presence of small-scale phase coherence. The coherence seems to be sufficiently strong to break the adiabatic invariance of helicity. The nature of the observed fluctuations suggests that the invariance properties of helicity may not be held responsible for the buildup of the correlations. In the light of these results it is questionable whether helicity fluctuations can play a fundamental role in the organization or characterization of turbulent structures.