Shallow Water Waves A Comparison of Theories and Experiments

Méhauté, Bernard Le; Divoky, David; Lin, Albert Chin-Yuh

doi:10.1061/9780872620131.007

Cited by 25 publications

(25 citation statements)

References 11 publications

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“…There is a reasonable agreement between the data and mathematical functions, although neither the linear wave theory nor the Boussinesq equations capture the asymmetrical wave shape nor the fine details of the free-surface profile shape. The findings are consistent with an earlier study of relatively large amplitude shallow water waves [35]. Further the experimental observations highlight the asymmetry of the free-surface undulations, with some differences in wave shape from crest to trough and from trough to crest.…”

Section: Undular Tidal Boressupporting

confidence: 91%

Current knowledge in tidal bores and their environmental, ecological and cultural impacts

Chanson

2009

Environ Fluid Mech

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A tidal bore is a series of waves propagating upstream as the tidal flow turns to rising. It forms during the spring tide conditions when the tidal range exceeds 5-6 m and the flood tide is confined to a narrow funnelled estuary with low freshwater levels. A tidal bore is associated with a massive mixing of the estuarine waters that stirs the organic matter and creates some rich fishing grounds. Its occurrence is essential to many ecological processes and the survival of unique eco-systems. The tidal bore is also an integral part of the cultural heritage in many regions: the Qiantang River bore in China, the Severn River bore in UK, the Dordogne River in France. In this contribution, the environmental, ecological and cultural impacts of tidal bores are reviewed, explained and discussed.

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Section: Undular Tidal Boressupporting

confidence: 91%

Current knowledge in tidal bores and their environmental, ecological and cultural impacts

Chanson

2009

Environ Fluid Mech

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“…The adoption of an adequate truncation order N is in fact a potential criticism of all formulations of Fourier wave theory, including that recommended by Huang 16 and 32, the results being indistinguishable from the Cokelet tablesZ at N = 32 in shallow water and at N = 8 in deep water. That N rather than M is the crucial parameter has been confirmed in a rather more detailed analysis by Sobey,17 which has shown that the Fenton choice of M = N is appropriate provided that N is adequate for the particular steady wave solution.…”

Section: Fenton Formulationmentioning

confidence: 72%

“…The unknown variables in a Fourier wave solution are k, ti, C , or C,, Q, R, q, for m=O (l)M and (16) and the dynamic free surface boundary condition (DFSBC) at each of the free surface nodes Note in particular the use of the trapezoidal rule in equation (13) for the MWL. This is an exact result for the continuous integral in equation (7), where q ( x ) is represented by a truncated Fourier series, as is implied by equation (10).…”

Section: Fourier Approximation Wave Theorymentioning

confidence: 99%

Variations on Fourier wave theory

Sobey

1989

Numerical Methods in Fluids

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SUMMARYA review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.

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“…As the "wave speed' obtained previously is an integral quantity of the wave train (mean fluid velocity on a constant level), it might be expected that the details of actual flow fields would show somewhat poorer agreement. To examine this, comparisons were made with several of the experimental results for long waves of Le Mehaute, et al (6), to which several other wave theories have been previously applied. Results are shown in Fig.…”

Section: Comparison With Experiments and With Accurate Solutionsmentioning

confidence: 99%

A Fifth‐Order Stokes Theory for Steady Waves

Fenton

1985

J. Waterway, Port, Coastal, Ocean Eng.

573

302

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An alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself. The first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary, In addition to the usually specified design parameters of wave height, period and ~ water depth, it is also necessary to specify the current or mass flux to apply any steady wave theory. The reason being that the waves almost always travel on some finite current and the apparent wave period is actually a Dopplershifted period. Most previous theories have ignored this, and their application has been indefinite, if not wrong, at first order. A numerical method for testing theoretical results is proposed, which shows that two existing theories are wrong at fifth order, while the present theory and that of Chappelear are correct. Comparisons with experiments and accurate numerical results show that the present theory is accurate for wavelengths shorter than ten times the water depth.

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Shallow Water Waves A Comparison of Theories and Experiments

Cited by 25 publications

References 11 publications

Current knowledge in tidal bores and their environmental, ecological and cultural impacts

Current knowledge in tidal bores and their environmental, ecological and cultural impacts

Variations on Fourier wave theory

A Fifth‐Order Stokes Theory for Steady Waves

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