Cancellation exponents in helical and non-helical flows

PAOLA RODRIGUEZ IMAZIO; PABLO DANIEL MININNI

Dresden

Conferencia; Self-Organization in Turbulent Plasmas and Fluids, Summer School and Workshop; 2010

The Max Planck Institute for the Physics of Complex Systems

For turbulent flows it is well known that, as the energy, when present helicity cascades to smaller scales where it dissipates. It was first noted by Chen et al. that helicity and energy follow the same scaling law in the inertial range. However, the role played by helicity in the inertial range remains unclear. In helical flows helicity changes sign rapidly in space. Not being a positive definite quantity, global studies considering its spectral scaling in the inertial range are inconclusive, except for cases where one sign of helicity is dominant. We use the cancellation exponent to characterize the scaling laws followed by helicity fluctuations in numerical simulations of helical and non-helical turbulent flows, with different forcing functions and spanning a range of Reynolds numbers from 670 to 6200. The exponent can be related to the fractal dimension as well as to the first order helicity scaling exponent. The results are consistent with the geometry of helical structures being filamentary. Further analysis indicates that statistical properties of helicity fluctuations in the simulations do not depend on the global helicity of the flow.