Cancellation exponents in helical and non-helical flows

PAOLA RODRIGUEZ IMAZIO; PABLO DANIEL MININNI

Conferencia; School on Astrophysical Turbulence and Dynamos; 2009

The Abdus Salam International Centre for Theoretical Physics

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 spectrum 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 vpositive 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 helicityfluctuations 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 helicalstructures being filamentary. Further analysis indicates that statistical properties of helicity fluctuations in the simulations do not depend on the global helicity of the flow.