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q‐Advanced Models for Tsunami and Rogue Waves

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

Abstract

A wavelet Kq(t), that satisfies the q‐advanced differential equation Kq′(t)=Kq(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 Fq(t, x) = Kq(t)qSin(x). The profile Fq is similar to tsunami models in present use. The function Sin (t) q is a wavelet that satisfies a q‐advanced harmonic oscillator equation. It is also shown that another wavelet, Cos (t) 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 Kq and Cos q is examined on actual data.

Suggested Citation

Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:414060
DOI: 10.1155/2012/414060
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