Experiments on focusing unidirectional water waves

Abstract

Results of four groups of experiments involving transient, mechanically generated water waves in a narrow wave tank are described. The purpose of these experiments was to investigate the limitations of the validity of linear theory predictions of the spatiotemporal structure of the surface elevation in focal regions. For unidirectional surface gravity waves, focusing occurs as a result of long waves overtaking short waves. Surprisingly, in our measurements, nonlinear effects are stronger in deep water than in intermediate depth water and are stronger in nonfocusing wave trains than in focusing wave trains. These trends can be explained by the observation that the dominant source of nonlinear interaction in our measurements was the Benjamin-Feir instability, which acts only over a limited duration in focusing wave trains, only in wave trains whose bandwidth is narrow, and only in deep water. Under conditions in which the Benjamin-Feir instability does not act (as is expected to be the case in the ocean), predictions that take into account amplitude-dependent dispersion but otherwise neglect nonlinear effects are in good agreement with measurements for wave trains with (ka)max slightly in excess of 0.30. Copyright 2001 by the American Geophysical Union.