Kyung Doug Suh

Hyperbolic mild-slope equations extended to account for rapidly varying topography

Abstract In this paper, following the procedure outlined by Copeland [Copeland, G.J.M., 1985. A practical alternative to the mild-slope wave equation. Coastal Eng. 9, 125–149.] the elliptic extended refraction–diffraction equation of Massel [Massel, S.R., 1993. Extended refraction–diffraction equation for surface waves. Coastal Eng. 19, 97–126.] is recasted into the form of a pair of first-order equations, which constitute a hyperbolic system. The resultant model, which includes higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature, is merely an extension of the Copelands model to account for a rapidly varying topography. The importance of the higher-order bottom effect terms is examined in terms of relative water depth. The model developed is verified against other numerical or experimental results related to wave reflection from a plane slope with different inclination, from a patch of periodic ripples, and from an arc-shaped bar with different front angle. The relative importance of the higher-order bottom effect terms is also examined for these problems.

Separation of incident and reflected waves in wave-current flumes

Abstract A technique is developed to separate the incident and reflected waves propagating on a known current in a laboratory wave–current flume by analyzing wave records measured at two or more locations using a least squares method. It can be applied to both regular and irregular waves. To examine its performance, numerical tests are made for waves propagating on quiescent or flowing water. In some cases, to represent the signal noise and measurement error, white noise is superimposed on the numerically generated wave signal. For all the cases, good agreement is observed between target and estimation.

Reflection of irregular waves from perforated-wall caisson breakwaters

An analytical model has been developed that predicts the reflection of irregular waves normally incident upon a perforated-wall caisson breakwater. To examine the predictability of the developed model, laboratory experiments have been conducted for the reflection of irregular waves of various significant wave heights and periods impinging upon breakwaters having various wave chamber widths. For frequency-averaged reflection coefficients, though the overall agreement is fairly good between measurement and calculation, the model somewhat over-predicts the reflection coefficients at larger values, and under-predicts at smaller values. The model also underestimates the energy loss coefficients as wave reflection becomes larger. These differences occur because the model neglects the evanescent waves near the breakwater, which increase the energy loss at the perforated wall. The frequency-averaged reflection coefficient shows a minimum when the wave chamber width is approximately 0.2 times the significant wavelength, and it decreases with increasing wave steepness. Finally, it is shown that the reflection of irregular waves from a perforated-wall caisson breakwater depends on the wave frequency, so that the reflected wave spectrum shows a frequency dependent oscillatory behavior.

Experimental verification of horizontal two-dimensional modified mild-slope equation model

In order to verify modified mild-slope equation models in a horizontal two-dimensional space, a hydraulic experiment is made for surface wave propagation over a circular shoal on which water depth varies substantially. A horizontal two-dimensional numerical model is also constructed based on the hyperbolic equations that have been developed from the modified mild-slope equation to account for the substantial depth variation. Comparison between experimental measurements and numerical results shows that the modified mild-slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild-slope equation model gives large errors as the mild-slope assumption is violated.

Scattering of irregular waves by vertical cylinders

An analytical model has been developed that can predict the scattering of irregular waves normally incident upon an array of vertical cylinders. To examine the predictability of the developed model, laboratory experiments have been made for the reflection and transmission of irregular waves from arrays of circular cylinders with various diameters and gap widths. Though the overall agreement between measurement and calculation is fairly good, the model tends to over- and under-predict the reflection and transmission coefficients, respectively, as the gap width decreases. The model also underestimates the energy loss coefficients for small gap widths because it neglects the evanescent waves near the cylinders. The peaks of the measured spectra of the reflected and transmitted waves slightly shift towards higher frequencies compared with that of the incident wave spectrum probably because of the generation of shorter period waves due to the interference of the cylinders. Both model and experimental data show that the wave reflection and transmission become larger and smaller, respectively, as the wave steepness increases, which is a desirable feature of the cylinder breakwaters.

LABORATORY OBSERVATIONS OF TRIAD INTERACTION OF DEEP WATER WIND WAVES

The triad interactions have been known to be important only for shoaling waves or finite depth wind waves. In deep water, they are insignificant compared with the quadruplet interactions in respect to the evolution of wind waves due to energy transfer among the wave components. However, the triad interactions may be important even for deep water waves because they may closely be related to the wave steepness, which definitely affects wave breaking, drag of air flow over the sea, or navigation of ships, especially during the early stage of the development of wind waves. This study reports a series of laboratory experiments, whose data are subjected to bispectral analyses to investigate the triad interactions of deep-water wind waves. It is found that the bicoherence at the spectral peak frequency and the wave steepness are almost directly proportional, indicating that the steep waves with peaked crests and flat troughs are resulted from the triad interactions. Both bicoherence and wave steepness increase with the wave age during the early stage of wave generation and then drop off as the waves grow old. It seems that the energy of the secondary spectral peak developed by the triad interactions during the early stage of wave generation is redistributed to the neighboring frequencies by the quadruplet interactions during the later stage.