Cnoidal Waves in Shallow Water

Masch, Frank D.

doi:10.1061/9780872620056.001

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…energy flux such as expressed by equation (1). Masch (1964) was the ;:'s to d,,al with this subject; however, his wave theory is not consistc:.t, eve; erroneous, (in the table of functions used by Masch in the shoakn4 of cnudal wave, the water depth below MWL should be substitutea by ht, the hater depth under trough), and the results are presented in a form which is difficult to use. The relation to deepwater wave and sinusoidal theory is not discussed and no attempt is made to follow the shoaling of a specific wave.…”

Section: Instead Of Expressingmentioning

confidence: 99%

Transformation of Monochromatic Waves from Deep to Shallow Water

Méhauté¹,

Wang²

1980

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This report is published to provide coastal engineers with a formulation and a set of nomographs for determining the breaking wave characteristics, such as breaking wave height, depth of breaking, and angle of breaking wave with a straight shoreline, as functions of the deepwater wave characteristics: wave height, wave period, and wave angle. This formulation is necessary to determine the littoral drift transport; however, to obtain such results, a review of nonlinear wave transformation is presented. A "hybrid" wave approach based on linear (or Stokes third order) and cnoidal waves is proposed as the best theory from available experimental data. The work was carried out under the coastal structures program of the Coastal Engineering Research Center (CERC).

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Section: Instead Of Expressingmentioning

confidence: 99%

Transformation of Monochromatic Waves from Deep to Shallow Water

Méhauté¹,

Wang²

1980

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“…All these investigations on cnoidal waves are based on an energy flux such as expressed by equation (1). Masch (1964) was the first to deal with this subject; however, his wave theory is not consistent, even erroneous, (in the table of functions used by Masch in the shoaling of cnoidal wave, the water depth below NIWL should be substituted by ht , the water depth under trough) , and the results are presented in a form which is difficult to use.…”

Section: (B)mentioning

confidence: 99%

Transformation of monochromatic waves from deep to shallow water / by Bernard Le Mehaute and John D. Wang.

Méhauté¹,

Wang²

1980

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This report is published to provide coastal engineers with a formulation and a set of nomographs for determining the breaking wave characteristics, such as breaking wave height, depth of breaking, and angle of breaking wave with a straight shoreline, as functions of the deepwater wave characteristics wave height, wave period, and wave angle. This formulation is necessary to determine the littoral drift transport; however, to obtain such results, a review of nonlinear wave transformation is presented. A "hybrid" wave approach based on linear (or Stokes third order) and cnoidal waves is proposed as the best theory from available experimental data. The work was carried out under the coastal structures program of the Coastal Engineering Research Center (CERC) .

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“…The two classical Korteweg and de Vries (KDV) [1] and Boussinesq models (BM) [2], together with the nonlinear Airy wave theory [3], laid the foundation for the study of waves in shallow water. Cnoidal traveling waves, which are solutions to the equations of KDV and BM, have been detailed and presented in an easy-to-use form by Wiegel et al [4,5]. The main physical characteristics of waves, such as period and wavelength, celerity, phase speed and other properties, were presented in visible and tabular form.…”

Section: Introductionmentioning

confidence: 99%

Physics of Traveling Waves in Shallow Water Environment

Shugan

Kuznetsov

Saprykina

et al. 2021

Water

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We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

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Cnoidal Waves in Shallow Water

Cited by 5 publications

References 11 publications

Transformation of Monochromatic Waves from Deep to Shallow Water

Transformation of Monochromatic Waves from Deep to Shallow Water

Transformation of monochromatic waves from deep to shallow water / by Bernard Le Mehaute and John D. Wang.

Physics of Traveling Waves in Shallow Water Environment

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