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Cancellation exponents in helical and non-helical flows

Published online by Cambridge University Press:  09 April 2010

P. RODRIGUEZ IMAZIO  and
P. D. MININNI
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: [email protected]
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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
Information
Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 241 - 250
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Baerenzung, J., Politano, H., Ponty, Y. & Pouquet, A. 2008 Spectral modelling of turbulent flows and the role of helicity. Phys. Rev. E 77, 046303.CrossRefGoogle ScholarPubMed
Borue, V. & Orszag, S. A. 1997 Spectra in helical three-dimensional homogeneous isotropic turbulence. Phys. Rev. E 55, 7005–7009.CrossRefGoogle Scholar
Brissaud, A., Frisch, U., Léorat, J., Lesieur, M. & Mazure, A. 1973 Helicity cascades in fully developed isotropic turbulence. Phys. Fluids 16, 1366–1367.CrossRefGoogle Scholar
Bruno, R. & Carbone, V. 1997 Sign singularity of the magnetic helicity from in situ solar wind observations. Astrophys. J. 488, 482–487.Google Scholar
Chen, Q., Chen, S. & Eyink, G. 2003 a The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids. 15, 361–374.CrossRefGoogle Scholar
Chen, Q., Chen, S., Eyink, G. & Holm, D. 2003 b Intermittency and the joint cascade of energy and helicity. Phys. Rev. Lett. 90, 214503.CrossRefGoogle ScholarPubMed
Eyink, G. & Sreenivasan, K. 2006 Onsager and the theory of hydrodinamic turbulence. Rev. Mod. Phys. 78, 87–134.CrossRefGoogle Scholar
Farge, M., Pellegrino, G. & Schneider, K. 2001 Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets. Phys. Rev. Lett. 87, 054501.CrossRefGoogle ScholarPubMed
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Gomez, D. O. & Mininni, P. D. 2004 Understanding turbulence through numerical simulations. Physica A 342, 69–75.CrossRefGoogle Scholar
Holm, D. & Kerr, R. 2007 Helicity in the formation of turbulence. Phys. Fluids 19, 025101.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Acad. Nauk SSSR A 30, 301–305.Google Scholar
Kurien, S. 2003 The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation. Physica D 175, 167–176.CrossRefGoogle Scholar
Lilly, D. 1986 The structure, energetics and propagation of rotating convective storms. J. Atmos. Sci. 43, 126–140.2.0.CO;2>CrossRefGoogle Scholar
Mininni, P., Alexakis, A. & Pouquet, A. 2006 Large scale flow effects, energy transfer, and self-similarity on turbulence. Phys. Rev. E 74, 016303.CrossRefGoogle ScholarPubMed
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129.CrossRefGoogle Scholar
Moffat, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Moffatt, H. K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. J. Fluid Mech. 159, 359–378.CrossRefGoogle Scholar
Moffatt, H. K. & Tsinober, A. 1992 Helicity in laminar and turbulent flows. Annu. Rev. Fluid Mech. 24, 281–312.CrossRefGoogle Scholar
Ott, E., Du, Y., Sreenivasan, K., Juneja, A. & Suri, A. 1992 Sign-singular measures: fast magnetic dynamos, and high-Reynolds-number fluid turbulence. Phys. Rev. Lett. 69, 2654–2657.CrossRefGoogle ScholarPubMed
Pietarila Graham, J., Mininni, P. D. & Pouquet, A. 2005 Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modelling. Phys. Rev. E 72, 045301(R).CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354.CrossRefGoogle Scholar
Sorriso-Valvo, L., Carbone, B., Noullez, A., Politano, H., Pouquet, A. & Veltri, P. 2002 Analisys of cancellation in two-dimensional magnetohydrodinamic turbulence. Phys. Plasmas 9, 89–95.CrossRefGoogle Scholar
Vainshtein, S. I., Sreenivasan, K. R., Pierrehumbert, R. T., Kashyap, V. & Juneja, A. 1994 Scaling exponents for turbulence and other random processes and their relationships with multifractal structure. Phys. Rev. E 50, 1823–1835.CrossRefGoogle ScholarPubMed
Wilkin, L. S., Barenghi, C. F. & Shukurov, A. 2007 Magnetic structures produced by small-scale dynamos. Phys. Rev. Lett. 99, 134501.CrossRefGoogle Scholar