Cancellation exponents in helical and non-helical flows
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...
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todo:paper_00221120_v651_n_p241_Imazio2023-10-03T14:26:33Z Cancellation exponents in helical and non-helical flows Imazio, P.R. Mininni, P.D. Energy cascade First-order Forcing function Helical flows Helical structures Helicities Helicity cascades Numerical simulation Positive definite Quadratic invariant Scaling exponent Statistical properties Three dimensions Computer simulation Euler equations Reynolds number Fractal dimension Eulerian analysis flow velocity numerical model Reynolds number turbulent flow vorticity 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. © 2010 Cambridge University Press. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221120_v651_n_p241_Imazio |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Energy cascade First-order Forcing function Helical flows Helical structures Helicities Helicity cascades Numerical simulation Positive definite Quadratic invariant Scaling exponent Statistical properties Three dimensions Computer simulation Euler equations Reynolds number Fractal dimension Eulerian analysis flow velocity numerical model Reynolds number turbulent flow vorticity |
spellingShingle |
Energy cascade First-order Forcing function Helical flows Helical structures Helicities Helicity cascades Numerical simulation Positive definite Quadratic invariant Scaling exponent Statistical properties Three dimensions Computer simulation Euler equations Reynolds number Fractal dimension Eulerian analysis flow velocity numerical model Reynolds number turbulent flow vorticity Imazio, P.R. Mininni, P.D. Cancellation exponents in helical and non-helical flows |
topic_facet |
Energy cascade First-order Forcing function Helical flows Helical structures Helicities Helicity cascades Numerical simulation Positive definite Quadratic invariant Scaling exponent Statistical properties Three dimensions Computer simulation Euler equations Reynolds number Fractal dimension Eulerian analysis flow velocity numerical model Reynolds number turbulent flow vorticity |
description |
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. © 2010 Cambridge University Press. |
format |
JOUR |
author |
Imazio, P.R. Mininni, P.D. |
author_facet |
Imazio, P.R. Mininni, P.D. |
author_sort |
Imazio, P.R. |
title |
Cancellation exponents in helical and non-helical flows |
title_short |
Cancellation exponents in helical and non-helical flows |
title_full |
Cancellation exponents in helical and non-helical flows |
title_fullStr |
Cancellation exponents in helical and non-helical flows |
title_full_unstemmed |
Cancellation exponents in helical and non-helical flows |
title_sort |
cancellation exponents in helical and non-helical flows |
url |
http://hdl.handle.net/20.500.12110/paper_00221120_v651_n_p241_Imazio |
work_keys_str_mv |
AT imaziopr cancellationexponentsinhelicalandnonhelicalflows AT mininnipd cancellationexponentsinhelicalandnonhelicalflows |
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1782024247472816128 |