Computation of azimuthal waves and their stability in thermal convection in rotating spherical shells with application to the study of a double-Hopf bifurcation

A methodology to compute azimuthal waves, appearing in thermal convection of a pure fluid contained in a rotating spherical shell, and to study their stability is presented. It is based on continuation, Newton-Krylov, and Arnoldi methods. An application to the study of a double-Hopf bifurcation of t...

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Detalhes bibliográficos
Autores: Sánchez Umbría, Juan|||0000-0002-3271-8012, García González, Fernando|||0000-0003-4507-0486, Net Marcé, Marta|||0000-0002-8034-1854
Tipo de documento: artigo
Data de publicação:2013
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/19530
Acesso em linha:https://hdl.handle.net/2117/19530
https://dx.doi.org/10.1103/PhysRevE.87.033014
Access Level:Acceso aberto
Palavra-chave:Heat--Convection
Eigenvalues
Eigenfunctions
Ocean currents
Heat convection
Eigenvalues and eigenfunctions
Hopf bifurcation
Calor -- Convecció
Valors propis
Funcions pròpies
Corrents marins
Àrees temàtiques de la UPC::Física
Descrição
Resumo:A methodology to compute azimuthal waves, appearing in thermal convection of a pure fluid contained in a rotating spherical shell, and to study their stability is presented. It is based on continuation, Newton-Krylov, and Arnoldi methods. An application to the study of a double-Hopf bifurcation of the basic state is shown for Ekman and Prandtl numbers E=10−4 and σ=0.1, respectively, radius ratios η∈[0.32,0.35], Rayleigh numbers R∈[1.8×105,6×105], and nonslip and perfectly conducting boundary conditions. The knowledge of the bifurcation diagrams, including the unstable solutions, allows one to understand the coexistence of stable thermal Rossby waves of different azimuthal wave numbers at some parameter regions, and the origin of some new intermittent solutions found, as trajectories close to heteroclinic chains. Moreover, the structure of the eigenfunctions at the secondary bifurcations explains the existence of the amplitude and shape modulated waves.