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Article: Critical ratio between the amplitudes of two overtaking solitary water waves

TitleCritical ratio between the amplitudes of two overtaking solitary water waves
Authors
Issue Date2007
PublisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.org
Citation
Physical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2007, v. 75 n. 3 How to Cite?
AbstractIn this paper, we study the critical ratio between the amplitudes of two overtaking solitary waves on a layer of water with uniform depth. At the center of encounter, the wave profile is fore-and-aft symmetric, but it could have a single peak or double peaks. The critical ratio separates these two regimes. At the critical point, the wave peak is flat with zero slope and curvature. We solve the full water wave problem numerically by using a fully nonlinear and highly dispersive Boussinesq model. The model is numerically justified to be a good approximation of the Euler equations for solitary waves with very large amplitude. For small amplitude water waves, our calculated critical ratio reduces to the well-known result of 3 predicted by the Korteweg-de Vries equation, a weakly nonlinear and weakly dispersive model. For large amplitude water waves, the nonlinear effect is significant; we find that the critical ratio deviates significantly from 3. For water waves with very high amplitude, e.g., 0.6 relative wave height, the critical ratio could be as large as 4. Our result suggests that higher-order nonlinear and dispersive effects are important when modeling the strong interaction between large amplitude water waves. © 2007 The American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/177741
ISSN
2014 Impact Factor: 2.288
2015 SCImago Journal Rankings: 0.999
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Ben_US
dc.contributor.authorZhang, JEen_US
dc.contributor.authorZhang, Jen_US
dc.contributor.authorLiu, Hen_US
dc.date.accessioned2012-12-19T09:39:46Z-
dc.date.available2012-12-19T09:39:46Z-
dc.date.issued2007en_US
dc.identifier.citationPhysical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2007, v. 75 n. 3en_US
dc.identifier.issn1539-3755en_US
dc.identifier.urihttp://hdl.handle.net/10722/177741-
dc.description.abstractIn this paper, we study the critical ratio between the amplitudes of two overtaking solitary waves on a layer of water with uniform depth. At the center of encounter, the wave profile is fore-and-aft symmetric, but it could have a single peak or double peaks. The critical ratio separates these two regimes. At the critical point, the wave peak is flat with zero slope and curvature. We solve the full water wave problem numerically by using a fully nonlinear and highly dispersive Boussinesq model. The model is numerically justified to be a good approximation of the Euler equations for solitary waves with very large amplitude. For small amplitude water waves, our calculated critical ratio reduces to the well-known result of 3 predicted by the Korteweg-de Vries equation, a weakly nonlinear and weakly dispersive model. For large amplitude water waves, the nonlinear effect is significant; we find that the critical ratio deviates significantly from 3. For water waves with very high amplitude, e.g., 0.6 relative wave height, the critical ratio could be as large as 4. Our result suggests that higher-order nonlinear and dispersive effects are important when modeling the strong interaction between large amplitude water waves. © 2007 The American Physical Society.en_US
dc.languageengen_US
dc.publisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.orgen_US
dc.relation.ispartofPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsen_US
dc.titleCritical ratio between the amplitudes of two overtaking solitary water wavesen_US
dc.typeArticleen_US
dc.identifier.emailZhang, JE: jinzhang@hku.hken_US
dc.identifier.authorityZhang, JE=rp01125en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1103/PhysRevE.75.036608en_US
dc.identifier.pmid17500810-
dc.identifier.scopuseid_2-s2.0-33947191373en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33947191373&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume75en_US
dc.identifier.issue3en_US
dc.identifier.isiWOS:000245324700064-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridWang, B=13003214000en_US
dc.identifier.scopusauthoridZhang, JE=7601346659en_US
dc.identifier.scopusauthoridZhang, J=8291687000en_US
dc.identifier.scopusauthoridLiu, H=26643608700en_US

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