Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows

The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are...

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Autor principal:	Mininni, Pablo Daniel
Publicado:	2009
Materias:	Eddy viscosity Euler flows Galerkin Helical flows Helicity Helicity cascades High wave number Ideal flow Initial conditions Linear scaling Navier Stokes Small scale Thermalization Transient energy Transient evolution Wave numbers Dynamics Euler equations Viscosity Navier Stokes equations
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v79_n5_p_Krstulovic http://hdl.handle.net/20.500.12110/paper_15393755_v79_n5_p_Krstulovic
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v79_n5_p_Krstulovic
record_format	dspace
spelling	paper:paper_15393755_v79_n5_p_Krstulovic2023-06-08T16:20:41Z Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows Mininni, Pablo Daniel Eddy viscosity Euler flows Galerkin Helical flows Helicity Helicity cascades High wave number Ideal flow Initial conditions Linear scaling Navier Stokes Small scale Thermalization Transient energy Transient evolution Wave numbers Dynamics Euler equations Viscosity Navier Stokes equations The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are found using initial data concentrated at high wave numbers. Using low-wave-number initial conditions, the results of Cichowlas [Phys. Rev. Lett. 95, 264502 (2005)] are extended to helical flows. Similarities between the turbulent transient evolution of the ideal (time-reversible) system and viscous helical flows are found. Using an argument in the manner of Frisch [Phys. Rev. Lett. 101, 144501 (2008)], the excess of relative helicity found at small scales in the viscous run is related to the thermalization of the ideal flow. The observed differences in the behavior of truncated Euler and (constant viscosity) Navier-Stokes are qualitatively understood using the concept of eddy viscosity. The large scales of truncated Euler equations are then shown to follow quantitatively an effective Navier-Stokes dynamics based on a variable (scale dependent) eddy viscosity. © 2009 The American Physical Society. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v79_n5_p_Krstulovic http://hdl.handle.net/20.500.12110/paper_15393755_v79_n5_p_Krstulovic
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Eddy viscosity Euler flows Galerkin Helical flows Helicity Helicity cascades High wave number Ideal flow Initial conditions Linear scaling Navier Stokes Small scale Thermalization Transient energy Transient evolution Wave numbers Dynamics Euler equations Viscosity Navier Stokes equations
spellingShingle	Eddy viscosity Euler flows Galerkin Helical flows Helicity Helicity cascades High wave number Ideal flow Initial conditions Linear scaling Navier Stokes Small scale Thermalization Transient energy Transient evolution Wave numbers Dynamics Euler equations Viscosity Navier Stokes equations Mininni, Pablo Daniel Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
topic_facet	Eddy viscosity Euler flows Galerkin Helical flows Helicity Helicity cascades High wave number Ideal flow Initial conditions Linear scaling Navier Stokes Small scale Thermalization Transient energy Transient evolution Wave numbers Dynamics Euler equations Viscosity Navier Stokes equations
description	The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are found using initial data concentrated at high wave numbers. Using low-wave-number initial conditions, the results of Cichowlas [Phys. Rev. Lett. 95, 264502 (2005)] are extended to helical flows. Similarities between the turbulent transient evolution of the ideal (time-reversible) system and viscous helical flows are found. Using an argument in the manner of Frisch [Phys. Rev. Lett. 101, 144501 (2008)], the excess of relative helicity found at small scales in the viscous run is related to the thermalization of the ideal flow. The observed differences in the behavior of truncated Euler and (constant viscosity) Navier-Stokes are qualitatively understood using the concept of eddy viscosity. The large scales of truncated Euler equations are then shown to follow quantitatively an effective Navier-Stokes dynamics based on a variable (scale dependent) eddy viscosity. © 2009 The American Physical Society.
author	Mininni, Pablo Daniel
author_facet	Mininni, Pablo Daniel
author_sort	Mininni, Pablo Daniel
title	Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
title_short	Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
title_full	Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
title_fullStr	Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
title_full_unstemmed	Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
title_sort	cascades, thermalization, and eddy viscosity in helical galerkin truncated euler flows
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v79_n5_p_Krstulovic http://hdl.handle.net/20.500.12110/paper_15393755_v79_n5_p_Krstulovic
work_keys_str_mv	AT mininnipablodaniel cascadesthermalizationandeddyviscosityinhelicalgalerkintruncatedeulerflows
_version_	1768541672560394240

Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows

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