# Q-advanced models for tsunami and rogue waves

- ECU Author/Contributor (non-ECU co-authors, if there are any, appear on document)
- D. W.,Randriampiry,N.,Spurr,M. J. Pravica (Creator)
- Institution
- East Carolina University (ECU )
- Web Site: http://www.ecu.edu/lib/

**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.

## Additional Information

- Publication
- Other
- Language: English
- Date: 2012

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Q-advanced models for tsunami and rogue waves | http://hdl.handle.net/10342/7890 | The described resource references, cites, or otherwise points to the related resource. |