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Three-dimensional nonlinear solitary waves in shallow water generated by an advancing disturbance

Published online by Cambridge University Press:  31 October 2002

YILE LI
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
PAUL D. SCLAVOUNOS
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

The nonlinear long waves generated by a disturbance moving at subcritical, critical and supercritical speed in unbounded shallow water are investigated. The problem is formulated by a new modified generalized Boussinesq equation and solved numerically by an implicit finite-difference algorithm. Three-dimensional upstream solitary waves with significant amplitude are generated with a periodicity by a pressure distribution or slender strut advancing on the free surface. The crestlines of these solitons are almost perfect parabolas with decreasing curvature with respect to time. Behind the disturbance, a complicated, divergent Kelvin-like wave pattern is formed. It is found that, unlike the wave breaking phenomena in a narrow channel at Fh [ges ] 1.2, the three- dimensional upstream solitons form several parabolic water humps and are blocked ahead of the disturbance at supercritical speed in an unbounded domain for large time.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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