Shoaling of Cnoidal Waves

Svendson, Ib A.; Brink-Kjaer, O.

doi:10.9753/icce.v13.18

Cited by 22 publications

(42 citation statements)

References 2 publications

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“…These results are similar to those obtained by Iwagaki and Sakai (1972). The wave shoaling curves given in Figure 7 are compared with the shoaling curves based on cnoidal wave theory developed by Svendsen and Kjaer (1972) and stream function theory by Dean (1974). The comparison shows similar trends, height of shoaling as a function of H 0 /L 0 .…”

Section: Figure 5 -Wave Shoaling Testsupporting

confidence: 80%

Refraction of Finite-Height and Breaking Waves

Walker¹

1976

Int. Conf. Coastal. Eng.

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The primary objective of this study was to ascertain the influence of wave height and breaking on wave refraction over a three-dimensional shoal. The subject wave transformations were studied in an hydraulic model. Wave shoaling, decay in the breaker zone, and phase velocities were analyzed in a base test series over a bottom slope of 1:30. A second test series was conducted over a three-dimensional shoal. Wave patterns were photographed and wave heights and celerities were measured. The measurements were compared with wave refraction patterns and coefficients computed by analytical methods. Wave shoaling observed over the constant 1:30 slope was 25 percent greater than predicted by Airy theory at the breaking point for wave steepness H0/L0=.030 and 50 percent greater than predicted for H0/Lo = •002. Shoaling measurements were compared with other empirical data sets, confirming the inadequacy of commonly used practice using linear wave theory near the breaker zone. The celerity measurements indicated that the non-breaking celerity was given by C = (1+.25 H/d)Ca, where Ca is the Airy celerity. The discussion and results give a basic understanding of wave refraction near the breaker zone, supplementing analytical papers on refraction procedures using finite amplitude wave theories.

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Section: Figure 5 -Wave Shoaling Testsupporting

confidence: 80%

Refraction of Finite-Height and Breaking Waves

Walker¹

1976

Int. Conf. Coastal. Eng.

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“…Prior to wave breaking, both η crest and H/h generally increase as waves propagating on the mild slope, while η trough decreases with the shoaling distance. This is typical in the wave shoaling process in which the wave phase speed and wavelength decrease, while the wave height increases to conserve the wave energy flux (Stiassnie & Peregrine, 1980;Svendsen & Brink-Kjaer, 1972). Moreover, the cases with lower wave steepness exhibit a larger wave shoaling coefficient (H b /H i with H b and H i being the wave height at the breaking point and at the constant depth, respectively), equal to 1.27, 1.63, and 1.81 for Cases 1-3, respectively.…”

Section: Free Surface Elevationmentioning

confidence: 99%

Laboratory Observation of Turbulence and Wave Shear Stresses Under Large Scale Breaking Waves Over a Mild Slope

Hsu

Huang

et al. 2019

JGR Oceans

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Laboratory measurements of turbulent flow and shear stresses in a surf zone under monochromatic breaking waves in a large‐scale wave flume are presented. Waves with various surf similarity parameters were generated to break at nearly identical water depths over a 1/100 mild slope. Free surface elevations were measured along the plane beach. Velocities in a water column located at the breaking region were measured by acoustic Doppler velocimeters. Results from wave shoaling coefficient, breaking index, and images are inconsistent with the breaker type categorizations from the surf similarity parameter. This suggests that a modification of the surf similarity parameter for very mild slopes may be necessary. For the plunging breakers, the ensemble‐averaged results indicate that intense turbulence kinetic energy was initially generated by large eddies at the surface then transported to the bottom frequently. The instantaneous results demonstrate that the intermittency of turbulence kinetic energy near the bed was caused by large eddies generated by wave overturning and relatively smaller obliquely descending eddies. Moreover, the magnitude of the wave shear stress (WSS) is one order of magnitude larger than that of the turbulent shear stress, indicating that the effects of the bottom slope, wave breaking, and bed friction are significant in the surf zone. The sign of the time‐averaged WSS switched between positive and negative, depending on the occurrences of phase lag and phase lead of the vertical coherent velocity. It suggests that a change may be required in Zou et al.'s (2006, https://doi.org/10.1029/2005JC003300) theory on the formulation of wave‐breaking induced WSS.

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“…Two of the earlier efforts in the study of finite-amplitude wave transformation treated shoaling of cnoidal waves. Svendsen and Brink-Kjaer (1973) connected first-order cnoidal theory with linear theory to develop a wave shoaling equation. They imposed the requirement of a matching energy flux to connect the two theories.…”

Section: Literature Reviewmentioning

confidence: 99%

Coupling Stokes and Cnoidal Wave Theories in a Nonlinear Refraction Model

Hardy

Kraus

1988

Int. Conf. Coastal. Eng.

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An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

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Shoaling of Cnoidal Waves

Cited by 22 publications

References 2 publications

Refraction of Finite-Height and Breaking Waves

Refraction of Finite-Height and Breaking Waves

Laboratory Observation of Turbulence and Wave Shear Stresses Under Large Scale Breaking Waves Over a Mild Slope

Coupling Stokes and Cnoidal Wave Theories in a Nonlinear Refraction Model

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