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On the non-dimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves

Lookup NU author(s): Dr Adrian Constantin, Professor Robin Johnson

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Abstract

In this note we describe the underlying principles - and pitfalls - of the process of non-dimensionalising and scaling the equations that model the classical problem in water waves. In particular, we introduce the two fundamental parameters (associated with amplitude and with wave length) and show how they are used, independently, to represent different approximations (with corresponding different interpretations and applications). In addition, and most importantly, we analyse how these two parameters play a role in the derivation of the Korteweg-de Vries (KdV) equation, which then lead to predictions for the regions of physical space where solitons might be expected to appear. In particular, we address the issue of whether KdV theory can be used effectively to predict tsunamis. We argue that for tsunamis the propagation distances are much too short for KdV dynamics to develop.

Publication metadata

Author(s): Constantin A, Johnson RS

Publication type: Article

Publication status: Published

Journal: Journal of Nonlinear Mathematical Physics

Year: 2008

Volume: 15

Issue: 2

Pages: 58-73

Print publication date: 01/08/2008

ISSN (print): 1402-9251

ISSN (electronic): 1776-0852

Publisher: World Scientific Publishing Co. Pte. Ltd.

URL: http://dx.doi.org/10.2991/jnmp.2008.15.s2.5

DOI: 10.2991/jnmp.2008.15.s2.5

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