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Cancellation exponents in helical and non-helical flows

Published online by Cambridge University Press:  09 April 2010

P. RODRIGUEZ IMAZIO*
Affiliation:
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Buenos Aires 1428, Argentina
P. D. MININNI
Affiliation:
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Buenos Aires 1428, Argentina National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA
*
Email address for correspondence: paolaimazio@df.uba.ar

Abstract

Helicity is a quadratic invariant of the Euler equation in three dimensions. As the energy, when present helicity cascades to smaller scales where it dissipates. However, the role played by helicity in the energy cascade is still unclear. In non-helical flows, the velocity and the vorticity tend to align locally creating patches with opposite signs of helicity. Also 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.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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