Influence of bottom topography on long water waves

Florent Chazel

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 4, page 771-799
  • ISSN: 0764-583X

Abstract

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We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy introduced by Bona et al. [Arch. Rational Mech. Anal.178 (2005) 373–410], we derive new symetric asymptotic models for each regime. The solutions of these systems are proved to give good approximations of solutions of the water waves problem. These results hold for solutions that evanesce at infinity as well as for spatially periodic ones.

How to cite

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Chazel, Florent. "Influence of bottom topography on long water waves." ESAIM: Mathematical Modelling and Numerical Analysis 41.4 (2007): 771-799. <http://eudml.org/doc/250058>.

@article{Chazel2007,
abstract = { We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy introduced by Bona et al. [Arch. Rational Mech. Anal.178 (2005) 373–410], we derive new symetric asymptotic models for each regime. The solutions of these systems are proved to give good approximations of solutions of the water waves problem. These results hold for solutions that evanesce at infinity as well as for spatially periodic ones. },
author = {Chazel, Florent},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Water waves; uneven bottoms; bottom topography; long-wave approximation; asymptotic expansion; hyperbolic systems; Dirichlet-Neumann operator.; Zakharov formulation; Dirichlet-Neumann operator},
language = {eng},
month = {10},
number = {4},
pages = {771-799},
publisher = {EDP Sciences},
title = {Influence of bottom topography on long water waves},
url = {http://eudml.org/doc/250058},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Chazel, Florent
TI - Influence of bottom topography on long water waves
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 4
SP - 771
EP - 799
AB - We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy introduced by Bona et al. [Arch. Rational Mech. Anal.178 (2005) 373–410], we derive new symetric asymptotic models for each regime. The solutions of these systems are proved to give good approximations of solutions of the water waves problem. These results hold for solutions that evanesce at infinity as well as for spatially periodic ones.
LA - eng
KW - Water waves; uneven bottoms; bottom topography; long-wave approximation; asymptotic expansion; hyperbolic systems; Dirichlet-Neumann operator.; Zakharov formulation; Dirichlet-Neumann operator
UR - http://eudml.org/doc/250058
ER -

References

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