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The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments

Hammack, Joseph L. and Segur, Harvey (1974) The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments. Journal of Fluid Mechanics, 65 (2). pp. 289-314. ISSN 0022-1120. doi:10.1017/S002211207400139X.

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The Korteweg-de Vries (KdV) equation is tested experimentally as a model for moderate amplitude waves propagating in one direction in relatively shallow water of uniform depth. For a wide range of initial data, comparisons are made between the asymptotic wave forms observed and those predicted by the theory in terms of the number of solitons that evolve, the amplitude of the leading soliton, the asymptotic shape of the wave and other qualitative features. The KdV equation is found to predict accurately the number of evolving solitons and their shapes for initial data whose asymptotic characteristics develop in the test section of the wave tank. The accuracy of the leading-soliton amplitudes computed by the KdV equation could not be conclusively tested owing to the viscous decay of the measured wave amplitudes; however, a procedure is presented for estimating the decay in amplitude of the leading wave. Computations suggest that the KdV equation predicts the amplitude of the leading soliton to within the expected error due to viscosity (12%) when the non-decayed amplitudes are less than about a quarter of the water depth. Indeed, agreement to within about 20% is observed over the entire range of experiments examined, including those with initial data for which the non-decayed amplitudes of the leading soliton exceed half the fluid depth.

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Additional Information:Copyright © 1974 Cambridge University Press. Reprinted with permission. (Received 10 September 1973) The authors gratefully acknowledge the kind assistance of the faculties and staffs of the Mathematics Department at Clarkson College of Technology and the W.M. Keck Laboratory of Hydraulics and Water Resources at the California Institute of Technology. This research was supported by the National Science Foundation under Grants GK-2370, GK-24716 and GA-27727Al and the Office of Naval Research, U.S. Navy.
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ID Code:11021
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Deposited On:23 Jun 2008
Last Modified:08 Nov 2021 21:13

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