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-Advanced Models for Tsunami and Rogue Waves

Author

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  • D. W. Pravica
  • N. Randriampiry
  • M. J. Spurr

Abstract

A wavelet , that satisfies the q -advanced differential equation for , 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 . The profile is similar to tsunami models in present use. The function is a wavelet that satisfies a q -advanced harmonic oscillator equation. It is also shown that another wavelet, , 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 and is examined on actual data.

Suggested Citation

  • D. W. Pravica & N. Randriampiry & M. J. Spurr, 2012. "-Advanced Models for Tsunami and Rogue Waves," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-26, September.
    • Handle: RePEc:hin:jnlaaa:414060
    DOI: 10.1155/2012/414060
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