Q-advanced models for tsunami and rogue waves
dc.contributor.author | Pravica, D. W. | |
dc.contributor.author | Randriampiry, N. | |
dc.contributor.author | Spurr, M. J. | |
dc.date.accessioned | 2020-04-03T18:16:42Z | |
dc.date.available | 2020-04-03T18:16:42Z | |
dc.date.issued | 2012-05-21 | |
dc.description.abstract | A wavelet [subscript] Kq[/subscript] (t ) , that satisfies the q-advanced differential equation [superscript] K q [variant prime][/superscript] ( t ) =[subscript] K q[/subscript] (qt ) for q >1 , is used to model N-wave oscillations observed in tsunamis. Although q-advanced ODEs may seem nonphysical, we present an application that model tsunamis, in particular the Japanese tsunami of March 11, 2011, by utilizing a one-dimensional wave equation that is forced by [subscript] Fq[/subscript] ( t ,x ) =[subscript] Kq[/subscript] [subscript] (t )q[/subscript] Sin (x ) . The profile [subscript] F q[/subscript] is similar to tsunami models in present use. The function Sin [superscript] ( t ) [/superscript] q is a wavelet that satisfies a q-advanced harmonic oscillator equation. It is also shown that another wavelet, Cos [superscript] ( t ) [/superscript] q , matches a rogue-wave profile. This is explained in terms of a resonance wherein two small amplitude forcing waves eventually lead to a large amplitude rogue. Since wavelets are used in the detection of tsunamis and rogues, the signal-analysis performance of [subscript] K q[/subscript] and [superscript] Cos q [/superscript] is examined on actual data. | en_US |
dc.identifier.doi | 10.1155/2012/414060 | |
dc.identifier.uri | http://hdl.handle.net/10342/7890 | |
dc.title | Q-advanced models for tsunami and rogue waves | en_US |
dc.type | Article | en_US |
ecu.journal.issue | 414060 | en_US |
ecu.journal.name | Abstract and Applied Analysis | en_US |
ecu.journal.pages | 1-26 | en_US |
ecu.journal.volume | 2012 | en_US |
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