A Theoretical and Experimental Study of Precursor Solitary Waves Generated by Moving Disturbances

Abstract

This is a joint theoretical, numerical and experimental study of the recently identified resonance phenomenon whereby a forcing disturbance moving steadily with a transcritical velocity in shallow water can generate, periodically, a succession of solitary waves, advancing upstream of the disturbance. A series of numerical and laboratory experiments was carried out with a cambered topography serving as the forcing disturbance moving over the floor of a water layer with velocity U, or Fronde number $F = U/\sqrt {{g{{h}_{0}}}}$,where g is the acceleration of gravity and h _o the original uniform water depth. Within the transcritical range of about 0.4 < F < 1.2 tested, and over a range of disturbance amplitudes, a series of upstream advancing solitary waves were generated, one after another, while a train of weakly nonlinear and weakly dispersive waves developed downstream of the disturbances immediately behind a nearly constant but elongating depressed water surface. For a review of the history and literature on this subject, we refer to the recent work by Wu (1987).