Journal of Nonlinear Mathematical Physics

Volume 15, Issue Supplement 2, August 2008, Pages 58 - 73

On the Non-Dimensionalisation, Scaling and Resulting Interpretation of the Classical Governing Equations for Water Waves

Authors
Adrian Constantin, Robin Stanley Johnson
Corresponding Author
Adrian Constantin
Received 6 April 2008, Available Online 1 August 2008.
DOI
10.2991/jnmp.2008.15.s2.5How to use a DOI?
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.

Copyright
© 2008, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - Supplement 2
Pages
58 - 73
Publication Date
2008/08/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2008.15.s2.5How to use a DOI?
Copyright
© 2008, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Adrian Constantin
AU  - Robin Stanley Johnson
PY  - 2008
DA  - 2008/08/01
TI  - On the Non-Dimensionalisation, Scaling and Resulting Interpretation of the Classical Governing Equations for Water Waves
JO  - Journal of Nonlinear Mathematical Physics
SP  - 58
EP  - 73
VL  - 15
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s2.5
DO  - 10.2991/jnmp.2008.15.s2.5
ID  - Constantin2008
ER  -