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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Autor principal: Mininni, Pablo Daniel
Publicado: 2010
Materias:
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
turbulent flow
vorticity
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v651_n_p241_Imazio
http://hdl.handle.net/20.500.12110/paper_00221120_v651_n_p241_Imazio
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00221120_v651_n_p241_Imazio2023-06-08T14:45:56Z Cancellation exponents in helical and non-helical flows Mininni, Pablo Daniel 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v651_n_p241_Imazio 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
Mininni, Pablo Daniel
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.
author Mininni, Pablo Daniel
author_facet Mininni, Pablo Daniel
author_sort Mininni, Pablo Daniel
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
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v651_n_p241_Imazio
http://hdl.handle.net/20.500.12110/paper_00221120_v651_n_p241_Imazio
work_keys_str_mv AT mininnipablodaniel cancellationexponentsinhelicalandnonhelicalflows
_version_ 1768544582238208000

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