q‐Advanced Models for Tsunami and Rogue Waves

D. W. Pravica, N. Randriampiry and M. J. Spurr

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/414060

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:414060

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().