Asymptotic regimes of ridge and rift formation in a thin viscous sheet model

We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-si...

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Autores principales: Perazzo, Carlos Alberto, Gratton, Julio
Publicado: 2008
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Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v20_n4_p_Perazzo
http://hdl.handle.net/20.500.12110/paper_10706631_v20_n4_p_Perazzo
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spelling paper:paper_10706631_v20_n4_p_Perazzo2023-06-08T16:04:30Z Asymptotic regimes of ridge and rift formation in a thin viscous sheet model Perazzo, Carlos Alberto Gratton, Julio Asymptotic regimes Asymptotics Dam-breaks Dry region Linear phase Self-similar Thin viscous sheet Uniform layer Multiphase flow Asymptotic analysis Newtonian liquids Ocean currents Viscosity Separation Dams Ridge Rift Viscous dam Viscous sheet model Asymptotic analysis Dams Newtonian liquids Ocean currents Viscosity We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-similar regimes that occur in these processes. During the growth of a ridge, two self-similar stages occur; the first takes place in the initial linear phase, and the second is obtained for a large time. Initially, the width and the height of the ridge increase as t 1/2. For a very large time, the width grows as t 3/4, while the height increases as t 1/4. On the other hand, in the process of formation of a rift, there are three self-similar asymptotics. The initial linear phase is similar to that for ridges. The second stage corresponds to the separation of the current in two parts, leaving a dry region in between. Last, for a very large t, each of the two parts in which the current has separated approaches the self-similar viscous dam break solution. © 2008 American Institute of Physics. Fil:Perazzo, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gratton, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v20_n4_p_Perazzo http://hdl.handle.net/20.500.12110/paper_10706631_v20_n4_p_Perazzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic regimes
Asymptotics
Dam-breaks
Dry region
Linear phase
Self-similar
Thin viscous sheet
Uniform layer
Multiphase flow
Asymptotic analysis
Newtonian liquids
Ocean currents
Viscosity
Separation
Dams
Ridge
Rift
Viscous dam
Viscous sheet model
Asymptotic analysis
Dams
Newtonian liquids
Ocean currents
Viscosity
spellingShingle Asymptotic regimes
Asymptotics
Dam-breaks
Dry region
Linear phase
Self-similar
Thin viscous sheet
Uniform layer
Multiphase flow
Asymptotic analysis
Newtonian liquids
Ocean currents
Viscosity
Separation
Dams
Ridge
Rift
Viscous dam
Viscous sheet model
Asymptotic analysis
Dams
Newtonian liquids
Ocean currents
Viscosity
Perazzo, Carlos Alberto
Gratton, Julio
Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
topic_facet Asymptotic regimes
Asymptotics
Dam-breaks
Dry region
Linear phase
Self-similar
Thin viscous sheet
Uniform layer
Multiphase flow
Asymptotic analysis
Newtonian liquids
Ocean currents
Viscosity
Separation
Dams
Ridge
Rift
Viscous dam
Viscous sheet model
Asymptotic analysis
Dams
Newtonian liquids
Ocean currents
Viscosity
description We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-similar regimes that occur in these processes. During the growth of a ridge, two self-similar stages occur; the first takes place in the initial linear phase, and the second is obtained for a large time. Initially, the width and the height of the ridge increase as t 1/2. For a very large time, the width grows as t 3/4, while the height increases as t 1/4. On the other hand, in the process of formation of a rift, there are three self-similar asymptotics. The initial linear phase is similar to that for ridges. The second stage corresponds to the separation of the current in two parts, leaving a dry region in between. Last, for a very large t, each of the two parts in which the current has separated approaches the self-similar viscous dam break solution. © 2008 American Institute of Physics.
author Perazzo, Carlos Alberto
Gratton, Julio
author_facet Perazzo, Carlos Alberto
Gratton, Julio
author_sort Perazzo, Carlos Alberto
title Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
title_short Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
title_full Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
title_fullStr Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
title_full_unstemmed Asymptotic regimes of ridge and rift formation in a thin viscous sheet model
title_sort asymptotic regimes of ridge and rift formation in a thin viscous sheet model
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v20_n4_p_Perazzo
http://hdl.handle.net/20.500.12110/paper_10706631_v20_n4_p_Perazzo
work_keys_str_mv AT perazzocarlosalberto asymptoticregimesofridgeandriftformationinathinviscoussheetmodel
AT grattonjulio asymptoticregimesofridgeandriftformationinathinviscoussheetmodel
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