Q-advanced models for tsunami and rogue waves
Pravica, D. W.; Randriampiry, N.; Spurr, M. J.
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.
Pravica, D. W., & Randriampiry, N., & Spurr, M. J.. (May 2012). Q-advanced models for tsunami and rogue waves. Abstract and Applied Analysis, (2012:414060), p.1-26. Retrieved from http://hdl.handle.net/10342/7890
Pravica, D. W., and Randriampiry, N., and Spurr, M. J.. "Q-advanced models for tsunami and rogue waves". Abstract and Applied Analysis. 2012:414060. (1-26.), May 2012. September 30, 2020. http://hdl.handle.net/10342/7890.
Pravica, D. W. and Randriampiry, N. and Spurr, M. J., "Q-advanced models for tsunami and rogue waves," Abstract and Applied Analysis 2012, no. 414060 (May 2012), http://hdl.handle.net/10342/7890 (accessed September 30, 2020).
Pravica, D. W., Randriampiry, N., Spurr, M. J.. Q-advanced models for tsunami and rogue waves. Abstract and Applied Analysis. May 2012; 2012(414060) 1-26. http://hdl.handle.net/10342/7890. Accessed September 30, 2020.