Dynamics of partially thermalized solutions of the Burgers equation

The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of...

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Autores principales: Clark Di Leoni, P., Mininni, P.D., Brachet, M.E.
Formato: JOUR
Materias:
Data flow analysis
Burgers equations
Finite dimensional
Inviscid flows
Localized structures
Spatiotemporal analysis
Thermalization
Thermalization process
Transient solutions
Partial differential equations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_2469990X_v3_n1_p_ClarkDiLeoni
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_2469990X_v3_n1_p_ClarkDiLeoni
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spelling todo:paper_2469990X_v3_n1_p_ClarkDiLeoni2023-10-03T16:41:26Z Dynamics of partially thermalized solutions of the Burgers equation Clark Di Leoni, P. Mininni, P.D. Brachet, M.E. Data flow analysis Burgers equations Finite dimensional Inviscid flows Localized structures Spatiotemporal analysis Thermalization Thermalization process Transient solutions Partial differential equations The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called "tygers." We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments. © 2018 American Physical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_2469990X_v3_n1_p_ClarkDiLeoni
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Data flow analysis
Burgers equations
Finite dimensional
Inviscid flows
Localized structures
Spatiotemporal analysis
Thermalization
Thermalization process
Transient solutions
Partial differential equations
spellingShingle Data flow analysis
Burgers equations
Finite dimensional
Inviscid flows
Localized structures
Spatiotemporal analysis
Thermalization
Thermalization process
Transient solutions
Partial differential equations
Clark Di Leoni, P.
Mininni, P.D.
Brachet, M.E.
Dynamics of partially thermalized solutions of the Burgers equation
topic_facet Data flow analysis
Burgers equations
Finite dimensional
Inviscid flows
Localized structures
Spatiotemporal analysis
Thermalization
Thermalization process
Transient solutions
Partial differential equations
description The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called "tygers." We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments. © 2018 American Physical Society.
format JOUR
author Clark Di Leoni, P.
Mininni, P.D.
Brachet, M.E.
author_facet Clark Di Leoni, P.
Mininni, P.D.
Brachet, M.E.
author_sort Clark Di Leoni, P.
title Dynamics of partially thermalized solutions of the Burgers equation
title_short Dynamics of partially thermalized solutions of the Burgers equation
title_full Dynamics of partially thermalized solutions of the Burgers equation
title_fullStr Dynamics of partially thermalized solutions of the Burgers equation
title_full_unstemmed Dynamics of partially thermalized solutions of the Burgers equation
title_sort dynamics of partially thermalized solutions of the burgers equation
url http://hdl.handle.net/20.500.12110/paper_2469990X_v3_n1_p_ClarkDiLeoni
work_keys_str_mv AT clarkdileonip dynamicsofpartiallythermalizedsolutionsoftheburgersequation
AT mininnipd dynamicsofpartiallythermalizedsolutionsoftheburgersequation
AT brachetme dynamicsofpartiallythermalizedsolutionsoftheburgersequation
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