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Observation of dispersive shock waves developing from initial depressions in shallow water
Publikationstyp
Journal Article
Date Issued
2016-10-15
Sprache
English
TORE-URI
Journal
Volume
333
Start Page
276
End Page
284
Citation
Physica D: Nonlinear Phenomena 333: 276-284 (2016)
Publisher DOI
Publisher
Elsevier
We investigate surface gravity waves in a shallow water tank, in the limit of long wavelengths. We report the observation of non-stationary dispersive shock waves rapidly expanding over a 90 m flume. They are excited by means of a wave maker that allows us to launch a controlled smooth (single well) depression with respect to the unperturbed surface of the still water, a case that contains no solitons. The dynamics of the shock waves are observed at different levels of nonlinearity equivalent to a different relative smallness of the dispersive effect. The observed undulatory behavior is found to be in good agreement with the dynamics described in terms of a Korteweg–de Vries equation with evolution in space, though in the most nonlinear cases the description turns out to be improved over the quasi linear trailing edge of the shock by modeling the evolution in terms of the integro-differential (nonlocal) Whitham equation.
Subjects
Dispersive shock waves
Korteweg–de Vries equation
Water waves
Whitham equation
DDC Class
000: Allgemeines, Wissenschaft