Transformation of a shoaling undular bore
We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg–de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its i...
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| Veröffentlicht in: | Journal of fluid mechanics 2012-10, Vol.709, p.371-395 |
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| container_title | Journal of fluid mechanics |
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| creator | El, G. A. Grimshaw, R. H. J. Tiong, W. K. |
| description | We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg–de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons – an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments. |
| doi_str_mv | 10.1017/jfm.2012.338 |
| format | Article |
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The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2012.338</identifier><identifier>CODEN: JFLSA7</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Asymptotic properties ; Earth sciences ; Earth, ocean, space ; Evolution ; Exact sciences and technology ; Fluid mechanics ; Marine and continental quaternary ; Mathematical analysis ; Mathematical models ; Modulation ; Shallow water ; Shock waves ; Solitons ; Surficial geology ; Topography ; Water flow ; Wave propagation ; Waveform analysis</subject><ispartof>Journal of fluid mechanics, 2012-10, Vol.709, p.371-395</ispartof><rights>Copyright © Cambridge University Press 2012</rights><rights>2014 INIST-CNRS</rights><rights>Copyright © Cambridge University Press 2012</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c436t-9e6ac4b829698875b06d1abad103fe28d0756d686f85ffe37b9a752e4e50c6b43</citedby><cites>FETCH-LOGICAL-c436t-9e6ac4b829698875b06d1abad103fe28d0756d686f85ffe37b9a752e4e50c6b43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0022112012003382/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27923,27924,55627</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26471459$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>El, G. 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Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments.</description><subject>Asymptotic properties</subject><subject>Earth sciences</subject><subject>Earth, ocean, space</subject><subject>Evolution</subject><subject>Exact sciences and technology</subject><subject>Fluid mechanics</subject><subject>Marine and continental quaternary</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Modulation</subject><subject>Shallow water</subject><subject>Shock waves</subject><subject>Solitons</subject><subject>Surficial geology</subject><subject>Topography</subject><subject>Water flow</subject><subject>Wave propagation</subject><subject>Waveform analysis</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqNkE1LxDAQhoMouH7c_AEFERTsmkmapDnK4hcseFnPYdoma5e2WZPtwX9vll1ExIOHYS7PvDPzEHIBdAoU1N3K9VNGgU05Lw_IBAqpcyULcUgmlDKWAzB6TE5iXFEKnGo1ITeLgEN0PvS4af2QeZdhFt89du2wzMahGTsMWeWDPSNHDrtoz_f9lLw9Pixmz_n89elldj_P64LLTa6txLqoSqalLkslKiobwAoboNxZVjZUCdnIUrpSOGe5qjQqwWxhBa1lVfBTcr3LXQf_Mdq4MX0ba9t1OFg_RgNKUQ5awT9QAM5Aa6UTevkLXfkxDOkRA1SLVMBYom53VB18jME6sw5tj-EzQWar2CTFZqvYJMUJv9qHYqyxc0ll3cbvGSaLdKXYLp_uY7GvQtss7c_tfwR_AUo6iAI</recordid><startdate>20121025</startdate><enddate>20121025</enddate><creator>El, G. 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| subjects | Asymptotic properties Earth sciences Earth, ocean, space Evolution Exact sciences and technology Fluid mechanics Marine and continental quaternary Mathematical analysis Mathematical models Modulation Shallow water Shock waves Solitons Surficial geology Topography Water flow Wave propagation Waveform analysis |
| title | Transformation of a shoaling undular bore |
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