Torsional solutions of convection in rotating fluid spheres

A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, accord...

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Autores: Sánchez Umbría, Juan|||0000-0002-3271-8012, Net Marcé, Marta|||0000-0002-8034-1854
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/129163
Acceso en línea:https://hdl.handle.net/2117/129163
https://dx.doi.org/10.1103/PhysRevFluids.4.013501
Access Level:acceso abierto
Palabra clave:Convection (Astrophysics)
Convection in rotating Nonlinear torsional
Convecció (Física)
Àrees temàtiques de la UPC::Física
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spelling Torsional solutions of convection in rotating fluid spheresSánchez Umbría, Juan|||0000-0002-3271-8012Net Marcé, Marta|||0000-0002-8034-1854Convection (Astrophysics)Convection in rotating Nonlinear torsionalConvecció (Física)Àrees temàtiques de la UPC::FísicaA numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small Pr. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time- and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for E=10-4 at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with Ra. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.20192019-01-2520192019-02-14journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/129163https://dx.doi.org/10.1103/PhysRevFluids.4.013501reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1291632026-05-27T15:37:01Z
dc.title.none.fl_str_mv Torsional solutions of convection in rotating fluid spheres
title Torsional solutions of convection in rotating fluid spheres
spellingShingle Torsional solutions of convection in rotating fluid spheres
Sánchez Umbría, Juan|||0000-0002-3271-8012
Convection (Astrophysics)
Convection in rotating Nonlinear torsional
Convecció (Física)
Àrees temàtiques de la UPC::Física
title_short Torsional solutions of convection in rotating fluid spheres
title_full Torsional solutions of convection in rotating fluid spheres
title_fullStr Torsional solutions of convection in rotating fluid spheres
title_full_unstemmed Torsional solutions of convection in rotating fluid spheres
title_sort Torsional solutions of convection in rotating fluid spheres
dc.creator.none.fl_str_mv Sánchez Umbría, Juan|||0000-0002-3271-8012
Net Marcé, Marta|||0000-0002-8034-1854
author Sánchez Umbría, Juan|||0000-0002-3271-8012
author_facet Sánchez Umbría, Juan|||0000-0002-3271-8012
Net Marcé, Marta|||0000-0002-8034-1854
author_role author
author2 Net Marcé, Marta|||0000-0002-8034-1854
author2_role author
dc.subject.none.fl_str_mv Convection (Astrophysics)
Convection in rotating Nonlinear torsional
Convecció (Física)
Àrees temàtiques de la UPC::Física
topic Convection (Astrophysics)
Convection in rotating Nonlinear torsional
Convecció (Física)
Àrees temàtiques de la UPC::Física
description A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small Pr. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time- and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for E=10-4 at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with Ra. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-25
2019
2019-02-14
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/129163
https://dx.doi.org/10.1103/PhysRevFluids.4.013501
url https://hdl.handle.net/2117/129163
https://dx.doi.org/10.1103/PhysRevFluids.4.013501
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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