Open AccessExperiments on focusing unidirectional water waves
Author(s) -
Brown Michael G.,
Jensen Atle
Publication year - 2001
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2000jc000584
Subject(s) - instability , amplitude , nonlinear system , mechanics , physics , surface wave , dispersion (optics) , train , mechanical wave , deep water , waves and shallow water , gravitational wave , wave propagation , gravity wave , wind wave , geology , optics , computational physics , longitudinal wave , oceanography , cartography , quantum mechanics , astrophysics , thermodynamics , geography
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.