A new complementary mild-slope equation

Kim, Jang Whan; Bai, Kwang June

doi:10.1017/s0022112004007840

Cited by 45 publications

(55 citation statements)

References 14 publications

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“…Recently, Athanassoulis and Belibassakis [1999] added a ‘sloping bottom mode’ to the local mode series expansion, which properly satisfies the Neuman bottom boundary condition. This approach was further explored by Chandrasekera and Cheung , [2001] and Kim and Bai , [2004]. Although the sloping‐bottom mode yields only small corrections for the wave height, it significantly improves the accuracy of the velocity field close to the bottom.…”

Section: Introductionmentioning

confidence: 99%

Evolution of surface gravity waves over a submarine canyon

et al. 2007

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[1] The effects of a submarine canyon on the propagation of ocean surface waves are examined with a three-dimensional coupled-mode model for wave propagation over steep topography. Whereas the classical geometrical optics approximation predicts an abrupt transition from complete transmission at small incidence angles to no transmission at large angles, the full model predicts a more gradual transition with partial reflection/ transmission that is sensitive to the canyon geometry and controlled by evanescent modes for small incidence angles and relatively short waves. Model results for large incidence angles are compared with data from directional wave buoys deployed around the rim and over Scripps Canyon, near San Diego, California, during the Nearshore Canyon Experiment (NCEX). Wave heights are observed to decay across the canyon by about a factor 5 over a distance shorter than a wavelength. However, a spectral refraction model predicts an even larger reduction by about a factor 10, because low-frequency components cannot cross the canyon in the geometrical optics approximation. The coupled-mode model yields accurate results over and behind the canyon. These results show that although most of the wave energy is refractively trapped on the offshore rim of the canyon, a small fraction of the wave energy 'tunnels' across the canyon. Simplifications of the model that reduce it to the standard and modified mild slope equations also yield good results, confirming that evanescent modes and high-order bottom slope effects are of minor importance for the energy transformation of waves propagating across depth contours at large oblique angles.

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Section: Introductionmentioning

confidence: 99%

Evolution of surface gravity waves over a submarine canyon

et al. 2007

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“…On the other hand, a similar approach was also presented by Kim and Bai. 28 They introduced a variational principle ͑or Hamilton's principle͒ in terms of the stream function theory. In this function, the continuity equation is satisfied, as well as the boundary condition on the sea bed.…”

Section: B Literature Surveymentioning

confidence: 99%

A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom

et al. 2006

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In this paper a complementary mild-slope equation ͑CMSE͒ is derived in order to investigate the transformation of progressive waves obliquely propagating over the sloping bottom more realistically. We introduce a new depth function which includes the wave refraction and the influence of the bottom slope ␣, perturbed to the second-order in the integral equation. A new depth-integrated mild-slope equation is derived, by using the above mentioned depth function, to model a time-harmonic motion of small amplitude waves in varying water depth. The simulated results reveal that the proposed model provides a significant improvement in the calculation of the wavenumber and the group velocity at different bottom slopes. With the increasing bottom slope, the discrepancies in the reflection coefficient of Bragg scattering between the analytical solution and the one calculated from the conventional mild-slope equation ͑MSE͒ and the modified MSE ͑MMSE͒ are seen to steadily increase. The group velocity of the waves, when compared with the conventional MSE and MMSE, also shows its dependence on the bottom slope and wave propagating angle. The present model is observed to be quite efficient in taking into account the effect of steeper bottom slope.

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“…A similar approach was also reported by Kim and Bai (2004). They derived a complementary MSE (CMSE) using Hamilton's principle in terms of the stream function.…”

Section: Introductionmentioning

confidence: 81%

WWM Extended to Account for Wave Diffraction on a Current Over a Rapidly Varying Topography

Hsu

Liau

et al. 2008

Volume 4: Ocean Engineering; Offshore Renewable Energy

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The WWM (wind wave model) is extended to describe wave refraction-diffraction for wind waves propagating over a rapidly varying seabed in the presence of current. The wave diffraction effect is introduced into the wave action balance equation through the correction of wavenumber and propagation velocities using a diffraction corrected parameter. The formulation is based on the mild-slope equation for wave refraction-diffraction with current effect for a rapidly varying sea bottom. The WWM was used for the numerical implementation based on a finite element scheme. The present model was tested for wave diffraction in a number of different cases, namely from an elliptical shoal on a wave tank, from a cylinder in the presence of a current and from a detached breakwater build on a sloping beach. The comparison of predictions with other numerical models and experiments show that the validity of the model for describing wave propagating over a rapidly varying bottom with current effect is satisfactory. The implementation of this phase-decoupled refraction-diffraction approximation in WWM shows capability of the present model can be used in most practical engineering situations.

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A new complementary mild-slope equation

Cited by 45 publications

References 14 publications

Evolution of surface gravity waves over a submarine canyon

Evolution of surface gravity waves over a submarine canyon

A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom

WWM Extended to Account for Wave Diffraction on a Current Over a Rapidly Varying Topography

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