A new Boussinesq method for fully nonlinear waves from shallow to deep water
A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the La...
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Published in | Journal of fluid mechanics Vol. 462; pp. 1 - 30 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
10.07.2002
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Subjects | |
Online Access | Get full text |
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Summary: | A new method valid for highly dispersive and highly nonlinear water waves is
presented. It combines a time-stepping of the exact surface boundary conditions with
an approximate series expansion solution to the Laplace equation in the interior
domain. The starting point is an exact solution to the Laplace equation given in
terms of infinite series expansions from an arbitrary z-level. We replace the
infinite series operators by finite series (Boussinesq-type) approximations involving up
to fifth-derivative operators. The finite series are manipulated to incorporate Padé
approximants providing the highest possible accuracy for a given number of terms.
As a result, linear and nonlinear wave characteristics become very accurate up to
wavenumbers as high as kh = 40, while the vertical variation of the velocity field
becomes applicable for kh up to 12. These results represent a major improvement
over existing Boussinesq-type formulations in the literature. A numerical model is
developed in a single horizontal dimension and it is used to study phenomena such
as solitary waves and their impact on vertical walls, modulational instability in deep
water involving recurrence or frequency downshift, and shoaling of regular waves up
to breaking in shallow water. |
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Bibliography: | PII:S0022112002008467 ark:/67375/6GQ-27373L4S-D istex:584D9A368B20FF2F8054A8122EF237EFAEFB2052 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/S0022112002008467 |