Kyung-Duck Suh

Extended mild-slope equation for random waves

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter [J. Fluid Mech. 291 (1995) 393] using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography.

An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit

Abstract An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457–459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunts solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed.

CALCULATION OF EXPECTED SLIDING DISTANCE OF BREAKWATER CAISSON CONSIDERING VARIABILITY IN WAVE DIRECTION

In this study, the reliability design method developed by Shimosako and Takahashi in 2000 for the calculation of the expected sliding distance of the caisson of a vertical breakwater is extended to take into account the variability in wave direction. The effects of directional spreading and the variation of deepwater principal wave direction about its design value were found to be minor compared with those of the obliquity of the deepwater design principal wave direction from the shore-normal direction. Reducing the significant wave height at the design site by 6% to correct the effect of wave refraction when using Godas model was found to be appropriate when the deepwater design principal wave direction was about 20 degrees. When we used the field data in a part of the east coast of Korea, taking the variability in wave direction into account reduced the expected sliding distance to about one third of that calculated without taking the variability in wave direction into account, and the required caisson width was reduced by about 10% at the maximum.

Regional projection of future extreme wave heights around Korean Peninsula

In this study, future changes in regional extreme wave heights around the Korean Peninsula are projected by using the results of an atmosphere general circulation model and a third-generation wave model. The direct use of the model output at each grid point is not appropriate even though high resolution of 20 km is used for the models. Therefore, the model output is grouped into six regions around the Korean Peninsula. The grouping approach is reasonable in assessing climate change effects with alleviated model uncertainty. The extreme wave heights are simulated for two climate periods of 1979–2003 (present climate) and 2075–2099 (future climate). The model results are validated by comparing the simulated wave heights for the present climate with observed and hindcasted wave data. The extreme wave heights for the future climate are then projected for different seasons and in different regions. The 50-year return wave height in summer is projected to increase in most regions, especially in the high-latitude Yellow Sea and the East Sea, while the wave height in winter is projected to decrease in all the regions, especially in the East Sea.

APPLICATION OF RELIABILITY DESIGN METHODS TO DONGHAE HARBOR BREAKWATER

Reliability design methods have been developed for breakwater designs since the mid-1980s. The reliability design method is classified into three categories depending on the level of probabilistic concepts being employed, i.e. Level 1, 2, and 3 methods. Each method gives results in different forms, but all of them can be expressed in terms of probability of failure so that the difference can be compared among the different methods. In this study, we apply the reliability design methods to the stability of armor blocks and sliding of caissons of the breakwater of Donghae Harbor located in the east coast of Korea, which was constructed by traditional deterministic design methods to be damaged in 1987 and reinforced in 1991. Analyses are made for the breakwaters before the damage and after the reinforcement. The allowable probability of failure of a Tetrapod armor layer of 50 years lifetime is proposed as 40% for existing stability formulas, whilst that for caisson sliding as 20% with the failure criterion for the cumulative sliding distance over the lifetime of 0.1 m. The probability of failure before the damage is much higher than the allowable value for both stability of armor blocks and sliding of caissons, indicating that the breakwater was under-designed. The probability of failure for the reinforced breakwater is lower than the allowable value, indicating that the breakwater became stable after the reinforcement. On the other hand, the results of different reliability design methods were in fairly good agreement, confirming that there is not much difference among the different methods.

Wave Damping over a Multilayered, Permeable Seabed

Abstract In this study, a wave-damping rate was derived for waves propagating over a multilayered, permeable seabed of finite depth. For a single-layer bed, a monogram is presented for the relationship between the wave-damping rate and the relative water depth for various depths of the permeable bed. The derived damping rate was used in the extended mild-slope equation to calculate wave dissipation over the permeable bed. For a single-layer bed, the result from the extended mild-slope equation model was compared with the result from the integral equation method and showed good agreement. The extended mild-slope equation model was also used to examine the wave transmission over a permeable shoal with a various number of layers, each with a different permeability. In general, short waves are more influenced by the permeability of the shoal than long waves unless the water depth is so great that the influence of the permeable bed on the surface water waves disappears. For a multilayered bed, the influences of the permeability of the upper layer on wave dissipation and transmission are more significant than those of the lower layers.

RELIABILITY ANALYSIS OF BREAKWATER ARMOR BLOCKS: CASE STUDY IN KOREA

In Korea, Tetrapods have been widely used to protect rubble mound breakwaters against erosion due to wave action. The deterministic design method has been used based on Hudson or van der Meer formula. In this study, we have performed reliability analyses for thus designed Tetrapod armors of 12 trade harbors and 8 coastal harbors in Korea. It is found that there is a linear relationship between the safety factor and the probability of failure; the larger the safety factor, the smaller the probability of failure. It is also found that the probability of failure during 50-year service lifetime is about 60% for the Tetrapod armors designed by the deterministic design method with the safety factor of 1.0. This finding seems to be natural since the encounter probability that a breakwater will experience storm waves greater than the design wave during its lifetime is 63% if the lifetime is set equal to the design return period. The results of this study could provide a guideline for determining the target probability of failure of Tetrapod armors in the future. A similar approach could be used for armor units other than Tetrapods.

CALCULATION OF PARTIAL SAFETY FACTORS OF BREAKWATER ARMOR STONES CONSIDERING CORRELATION BETWEEN WAVE HEIGHT AND WAVE STEEPNESS

In calculating the partial safety factors of breakwater armor stones, it has been assumed that all the design variables are independent of one another. However, some of them are not independent but are correlated to each other. In the present study, the partial safety factors are calculated by considering the correlation between wave height and wave steepness. Smaller partial safety factors and smaller armor weight are obtained if the correlation is taken into account. The reduction becomes prominent as the probability of failure decreases (or the design armor weight increases). The correlation between wave height and steepness in real sea is also estimated by using the wave hindcasting data around the Korean Peninsula.

Wave-Induced Reynolds Stress in Three-Dimensional Nearshore Currents Model

ABSTRACT Chun, H. and Suh, K.-D., 2016. Wave-induced Reynolds stress in three-dimensional nearshore currents model. This paper presents the formulation of the wave-induced Reynolds stress (WIRS), i.e. the correlation of horizontal and vertical water particle velocities, based on the Airys wave theory. Even though the correlation of the velocities is zero in a constant-depth water, it has a nonzero value if there are slopes on the bottom and mean water level. Comparison of the vertical gradient of the WIRS term with the horizontal gradient of wave-forcing terms shows that the two terms have the same order of magnitude, which in turn is comparable to that of the radiation stress in the surf zone. For the three-dimensional computation of nearshore currents, the WIRS term is incorporated into a three-dimensional ocean model in the σ coordinates. The numerical model is then applied to two laboratory experiments. To see the effect of the WIRS term on the mean flow, numerical simulations without this term are also carried out. The numerical simulations show that the WIRS term influences the flow properties such as mean water level, longshore current, and undertow.

Estimation of Deepwater Design Wave Height on Southern Coast of Korean Peninsula by Empirical Simulation Technique

Estimation of wave height is the most important factor in the design of coastal structures such as breakwaters. In the present study, typhoon wind distribution was constructed by applying the parametric model of Holland (1980), and numerical simulations on the typhoon-generated waves were carried out using the WAM. The typhoons which affected the southern coast of the Korean Peninsula and several hypothetical typhoons were selected to construct the training sets. Design wave heights were estimated using the empirical simulation technique for various return periods and wave directions. The estimated design wave heights were compared with those by the peaks-over-threshold method and the results of KORDI(2005).