On new erosion models of Savage-Hutter type for avalanches

In this work, we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressibl...

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Autores: Bouchut, François, Fernández Nieto, Enrique Domingo, Mangeney, Anne, Lagreé, P.-Y.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2008
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32093
Acceso en línea:http://hdl.handle.net/11441/32093
https://doi.org/10.1007/s00707-007-0534-9
Access Level:acceso abierto
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repository_id_str
spelling On new erosion models of Savage-Hutter type for avalanchesBouchut, FrançoisFernández Nieto, Enrique DomingoMangeney, AnneLagreé, P.-Y.In this work, we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations. This model has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system. It has physically relevant steady state solutions, and, for constant slope, it gives a particular exact solution to the incompressible hydrostatic Euler equations. Then, we propose a simplified model, for which the energy conservation holds only up to third-order terms. Its associated eigenvalues depend on the mass exchange velocity between the static and moving layers. We show that a simplification used in some previously proposed models gives a non-consistent energy equation. Our models do not use, nor provide, any equation for the moving interface, thus other arguments have to be used in order to close the system. With special assumptions, and in particular small velocity, we can nevertheless obtain an equation for the evolution of the interface. Furthermore, the unknown parameters of the model proposed by Bouchaud et al. (J Phys Paris I 4,1383–1410, 1994) can be derived. For the quasi-stationary case we compare and discuss the equation for the moving interface with Khakhar’s model (J Fluid Mech 441,225–264, 2001).SpringerMatemática Aplicada I2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/32093https://doi.org/10.1007/s00707-007-0534-9reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésActa mechanica, 198, pp.181-208DOI 10.1007/s00707-007-0534-9info:eu-repo/semantics/openAccessoai:idus.us.es:11441/320932026-06-17T12:51:07Z
dc.title.none.fl_str_mv On new erosion models of Savage-Hutter type for avalanches
title On new erosion models of Savage-Hutter type for avalanches
spellingShingle On new erosion models of Savage-Hutter type for avalanches
Bouchut, François
title_short On new erosion models of Savage-Hutter type for avalanches
title_full On new erosion models of Savage-Hutter type for avalanches
title_fullStr On new erosion models of Savage-Hutter type for avalanches
title_full_unstemmed On new erosion models of Savage-Hutter type for avalanches
title_sort On new erosion models of Savage-Hutter type for avalanches
dc.creator.none.fl_str_mv Bouchut, François
Fernández Nieto, Enrique Domingo
Mangeney, Anne
Lagreé, P.-Y.
author Bouchut, François
author_facet Bouchut, François
Fernández Nieto, Enrique Domingo
Mangeney, Anne
Lagreé, P.-Y.
author_role author
author2 Fernández Nieto, Enrique Domingo
Mangeney, Anne
Lagreé, P.-Y.
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
description In this work, we study the modeling of one-dimensional avalanche flows made of a moving layer over a static base, where the interface between the two can be time dependent. We propose a general model, obtained by looking for an approximate solution with constant velocity profile to the incompressible Euler equations. This model has an energy dissipation equation that is consistent with the depth integrated energy equation of the Euler system. It has physically relevant steady state solutions, and, for constant slope, it gives a particular exact solution to the incompressible hydrostatic Euler equations. Then, we propose a simplified model, for which the energy conservation holds only up to third-order terms. Its associated eigenvalues depend on the mass exchange velocity between the static and moving layers. We show that a simplification used in some previously proposed models gives a non-consistent energy equation. Our models do not use, nor provide, any equation for the moving interface, thus other arguments have to be used in order to close the system. With special assumptions, and in particular small velocity, we can nevertheless obtain an equation for the evolution of the interface. Furthermore, the unknown parameters of the model proposed by Bouchaud et al. (J Phys Paris I 4,1383–1410, 1994) can be derived. For the quasi-stationary case we compare and discuss the equation for the moving interface with Khakhar’s model (J Fluid Mech 441,225–264, 2001).
publishDate 2008
dc.date.none.fl_str_mv 2008
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/32093
https://doi.org/10.1007/s00707-007-0534-9
url http://hdl.handle.net/11441/32093
https://doi.org/10.1007/s00707-007-0534-9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Acta mechanica, 198, pp.181-208
DOI 10.1007/s00707-007-0534-9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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