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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“…This is overcome by making an empirically based assumption that the still water level (Z=0) occurs roughly one-third ofthe vertical distance from trough to crest. This assumption, although not strictly valid across all wave types, is commonly observed in laboratory (Flick, Guza, and Inman, 1981) and higher-order, nonlinear wave theory (i.e.. Le Méhauté, Divoky, and Lin, 1968) where vertical asymmetry develops in a propagating waveform before breaking with a narrower, high crest and wider low trough. Results presented in Table 4 show the effect of altemative definitions of break point on the derived breaking wave height.…”

Section: Errors and Uncertaintymentioning

confidence: 92%

Automated Detection of Breaking Wave Height Using an Optical Technique

Shand

Bailey

Shand

2011

Journal of Coastal Research

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I www.JCRonline.org SHAND, T.D.; BAILEY, D.G., and SHAND, R.D., 2012. Automated detection of breaking wave height using an optical technique. Journal of Coastal Research, 28(3), 671-682. West Palm Beach (Florida), ISSN 0749-0208.Obtaining accurate information of nearshore wave characteristics including the position and height of individual breaking waves is essential to understanding the drivers of coastal processes, for engineering design and hazard prediction. Demand for such information in real time for recreational planning and hazard assessment is also high. Remote optical techniques would offer considerahle economic and spatial coverage advantages over conventional in situ instrumentation. However, optical methods for obtaining wave height information have been slow to develop and those available remain computationally expensive and require "favourable" environmental conditions. This paper presents a relatively simple yet robust approach to detecting and quantifying breaking wave position and height across a wide surf zone using a twin video camera configuration coupled with an image time-stack analysis approach. A numerical algorithm, HbSTACK, is developed and successfully tested under the environmental conditions experienced during field trials. Errors and uncertainties may arise in both the photogrammetric transformation from pixels to real-world coordinates and in the detection of wave crest and trough positions. These errors have been assessed using both field verification of the transformation model and manually detected crest and trough locations by experienced practitioners. Errors in output wave heights were thus estimated to be less than 1%.ADDITIONAL INDEX WORDS: Wave height. Wave breaking. Surf zone. Optical detection.

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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

Automated Detection of Breaking Wave Height Using an Optical Technique

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