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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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
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2008
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10706631_v20_n4_p_Perazzo |
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paperaa:paper_10706631_v20_n4_p_Perazzo2023-06-12T16:49:23Z Asymptotic regimes of ridge and rift formation in a thin viscous sheet model Phys. Fluids 2008;20(4) Perazzo, C.A. Gratton, J. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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, C.A. Gratton, J. 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. |
| format |
Artículo Artículo publishedVersion |
| author |
Perazzo, C.A. Gratton, J. |
| author_facet |
Perazzo, C.A. Gratton, J. |
| author_sort |
Perazzo, C.A. |
| 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 |
http://hdl.handle.net/20.500.12110/paper_10706631_v20_n4_p_Perazzo |
| work_keys_str_mv |
AT perazzoca asymptoticregimesofridgeandriftformationinathinviscoussheetmodel AT grattonj asymptoticregimesofridgeandriftformationinathinviscoussheetmodel |
| _version_ |
1769810190399438848 |