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Article: Roll waves on a shallow layer of mud modelled as a power-law fluid

TitleRoll waves on a shallow layer of mud modelled as a power-law fluid
Authors
Issue Date1994
PublisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=FLM
Citation
Journal Of Fluid Mechanics, 1994, v. 263, p. 151-183 How to Cite?
AbstractWe give a theory of permanent roll waves on a shallow layer of fluid mud which is modelled as a power-law fluid. Based on the long-wave approximation, Karman's momentum integral method is applied to derive the averaged continuity and the momentum equations. Linearized instability analysis of a uniform flow shows that the growth rate of unstable disturbances increases monotonically with the wavenumber, and therefore is insufficient to suggest a preferred wavelength for the roll wave. Nonlinear roll waves are obtained next as periodic shocks connected by smooth profiles with depth increasing monotonically from the rear to the front. Among all wavelengths only those longer than a certain threshold correspond to positive energy loss across the shock, and are physically acceptable. This threshold also implies a minimum discharge, viewed in the moving system, for the roll wave to exist. These facts suggest that a roll wave developed spontaneously from infinitesimal disturbances should have the shortest wavelength corresponding to zero dissipation across the shock, though finite dissipation elsewhere. The discontinuity at the wave front is a mathematical shortcoming needing a local requirement. Predictions for the spontaneously developed roll waves in a Newtonian case are compared with available experimental data. Longer roll waves, with dissipation at the discontinuous fronts, cannot be maintained if the uniform flow is linearly stable, when the fluid is slightly non-Newtonian. However, when the fluid is highly non-Newtonian, very long roll waves may still exist even if the corresponding uniform flow is stable to infinitesimal disturbances. Numerical results are presented for the phase speed, wave height and wavenumber, and wave profiles for a representative value of the flow index of fluid mud.
Persistent Identifierhttp://hdl.handle.net/10722/156401
ISSN
2015 Impact Factor: 2.514
2015 SCImago Journal Rankings: 1.450

 

DC FieldValueLanguage
dc.contributor.authorNg, ChiuOnen_US
dc.contributor.authorMei, Chiang Cen_US
dc.date.accessioned2012-08-08T08:42:17Z-
dc.date.available2012-08-08T08:42:17Z-
dc.date.issued1994en_US
dc.identifier.citationJournal Of Fluid Mechanics, 1994, v. 263, p. 151-183en_US
dc.identifier.issn0022-1120en_US
dc.identifier.urihttp://hdl.handle.net/10722/156401-
dc.description.abstractWe give a theory of permanent roll waves on a shallow layer of fluid mud which is modelled as a power-law fluid. Based on the long-wave approximation, Karman's momentum integral method is applied to derive the averaged continuity and the momentum equations. Linearized instability analysis of a uniform flow shows that the growth rate of unstable disturbances increases monotonically with the wavenumber, and therefore is insufficient to suggest a preferred wavelength for the roll wave. Nonlinear roll waves are obtained next as periodic shocks connected by smooth profiles with depth increasing monotonically from the rear to the front. Among all wavelengths only those longer than a certain threshold correspond to positive energy loss across the shock, and are physically acceptable. This threshold also implies a minimum discharge, viewed in the moving system, for the roll wave to exist. These facts suggest that a roll wave developed spontaneously from infinitesimal disturbances should have the shortest wavelength corresponding to zero dissipation across the shock, though finite dissipation elsewhere. The discontinuity at the wave front is a mathematical shortcoming needing a local requirement. Predictions for the spontaneously developed roll waves in a Newtonian case are compared with available experimental data. Longer roll waves, with dissipation at the discontinuous fronts, cannot be maintained if the uniform flow is linearly stable, when the fluid is slightly non-Newtonian. However, when the fluid is highly non-Newtonian, very long roll waves may still exist even if the corresponding uniform flow is stable to infinitesimal disturbances. Numerical results are presented for the phase speed, wave height and wavenumber, and wave profiles for a representative value of the flow index of fluid mud.en_US
dc.languageengen_US
dc.publisherCambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=FLMen_US
dc.relation.ispartofJournal of Fluid Mechanicsen_US
dc.titleRoll waves on a shallow layer of mud modelled as a power-law fluiden_US
dc.typeArticleen_US
dc.identifier.emailNg, ChiuOn:cong@hku.hken_US
dc.identifier.authorityNg, ChiuOn=rp00224en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0028384797en_US
dc.identifier.volume263en_US
dc.identifier.spage151en_US
dc.identifier.epage183en_US
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridNg, ChiuOn=7401705594en_US
dc.identifier.scopusauthoridMei, Chiang C=7103364150en_US

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