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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  and
PAUL D. SCLAVOUNOS
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
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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
Information
Journal of Fluid Mechanics , Volume 470 , 10 November 2002 , pp. 383 - 410
Copyright
© 2002 Cambridge University Press

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