Journal of Fluid Mechanics

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

a1 Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA


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 [gt-or-equal, slanted] 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.

(Received November 13 2001)
(Revised April 12 2002)