Helicity within the Kolmogorov Phenomenology of Turbulence

Abstract

In a phenomenology in which both energy and helicity exhibit net flux to the small scales it is natural to investigate how they might influence each other. Motivated by Kraichnan’s 1971 derivation of spectral scaling laws using the timescale for energy transfer in wavenumber, we proceed by considering the timescale for helicity transfer and its potential impact on energy distribution in wavenumber. We demonstrate using resolved direct numerical simulations that the predicted effects of a second timescale related to helicity transfer are consistent with observed statistics. Both the energy and helicity spectra show to close to a k-4/3 scaling in the higher wavenumber ‘bottleneck’ regime of the inertial range. The latter scaling is in agreement with our prediction for the scaling exponent based on a helicity-dependent timescale for twisting rather than shearing motions.