Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

Publication: Research - peer-reviewJournal article – Annual report year: 1999

View graph of relations

This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary conditions. It is demonstrated that previous fully dispersive formulations from the literature have used an inconsistent linear relation between the velocity potential and the surface elevation. As a consequence these formulations are accurate only in shallow water, while nonlinear transfer of energy is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement with the measurements, and it is found that the accuracy of e.g., the energy spectrum and of the third-order statistics is considerably improved by the new formulations, particularly outside the shallow-water range. (C) 1999 Elsevier Science B.V. All rights reserved.
Original languageEnglish
JournalCoastal Engineering
Publication date1999
Volume38
Journal number1
Pages1-24
ISSN0378-3839
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 17
Download as:
Download as PDF
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
PDF
Download as HTML
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
HTML
Download as Word
Select render style:
APAAuthorCBEHarvardMLAStandardVancouverShortLong
Word

ID: 5379835