• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.434-441
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• 2012

An analytic solution to the extended mild-slope equation was derived for waves propagating over an axi-symmetric pit. The water depth inside the pit was in proportion to a power of radial distance from the center of pit. The equation was transformed into the ordinary differential equation using the method of separation of variables. The coefficients of differential terms were expressed as an explicit form composing of the phase and group velocities. The bottom curvature and the square of bottom slope terms, which were added to the extended mild-slope equation, were expressed as power series. Finally, using the Frobenius series, the analytic solution to the extended mild-slope equation was derived. The present analytic solution was validated by comparing with the numerical solution obtained from FEM.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.4
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• pp.308-320
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• 2006

An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

• Journal of Korea Water Resources Association
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• v.40 no.11
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• pp.899-908
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• 2007

In this study, wave reflection due to depression of seabed is calculated by using eigenfunction expansion method. The proper numbers of steps and evanescent modes needed for analysis are suggested by applying the eigenfunction expansion method to bottom topography of which slope or curvature varies. While satisfying shallow or intermediate water depth condition, the optimal figure of depression of seabed is obtained by calculating reflection coefficient for various depressions of seabed. The reflection coefficient with distance between the depression of seabeds is then calculated after arraying the optimal geometry in two and three rows.

• Journal of Korea Water Resources Association
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• v.53 no.10
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• pp.871-876
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• 2020

Understanding the wave characteristics near the outlet of coastal power plants for cooling water in the vicinity of the dredged areas is critically important for the construction and operation of the plants. By Employing the eigenfunction expansion method, in this study, we analyzed the reflection of monochromatic water waves over (1) shear currents near the outlet and (2) multi-arrayed trenches representing dredged areas. We firstly optimized the number of grids expressing shear currents and the number of evanescent modes based on a convergence test. We then analyzed the sensitivity of the reflection coefficients depending on (1) magnitude of shear currents, (2) width of shear currents, (3) a distance between adjacent trenches, and (4) a number of trenches. The results showed that the reflection coefficient was more sensitive to the number of trenches and the distance between trenches than the velocity of shear currents and the width of shear currents. We also found that even the effect of shear currents is relatively small, the effect is not negligible in a relative water depth from shallow to near shallow water waves (0.01 < kh ≦ 0.70).

• Journal of Korea Water Resources Association
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• v.42 no.12
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• pp.1125-1133
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• 2009

Evanescent modes which are the other solutions of the Laplace equation for the linear dispersion equation may affect the wave transformation especially when a water depth varies abruptly. In this study, the effects of evanescent modes for a three-dimensional depression of seabed are investigated by using the eigenfunction expansion method. A convergence test is first carried out by changing numbers of domains and evanescent modes. The wave transformation for various depressions of seabed is then calculated under condition that the solution of the eigenfunction expansion method is converged.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.22-37
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• 2020

We analyze the comprehensive three-dimensional (3D) magnetic structure characteristics from the seafloor to the deep layer of the Tofua Arc (TA) 12 seamount in the Tonga Arc, Southwestern Pacific, using bathymetric and geomagnetic data, and magnetization vector inversion (MVI) results. The seafloor features surrounding TA 12 highlight a NW-SE-oriented elliptical caldera at the summit of the seamount, two small cones in the depressed area. A large-scale sea valley is present on the western flank of the seamount, extending from these caldera cones to the southwestern base of the seamount. TA 12 seamount exhibits a low magnetic anomaly in the caldera depression, whereas a high magnetic anomaly is observed surrounding the low magnetic anomaly across the caldera summit. It is therefore presumed that there may be a strong magnetic material distribution or magma intrusion in the caldera. The 3D MVI results show that the high anomaly zones are mainly present in the surrounding slopes of the seamount from the seafloor to the -3,000 m (below the seafloor) level, with the magnetic susceptibility intensity increasing as the seafloor level increases at the caldera depression. However, small high anomaly zones are present across the study area near the seafloor level. Therefore, we expect that the magma ascent in TA 12 seamount migrated from the flanks to the depression area. Furthermore, we assume that the complex magnetic distribution near the seafloor is due to the remnant magnetization.

• Journal of the Korean Geophysical Society
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• v.9 no.4
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• pp.409-416
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• 2006

Reflection seismic survey has been conducted using R/V Yuzmogeologia of Russia on the area of between northern part of Powell basin and South Scotia Ridge. 48-channel seismic data have been processed using Promax system. Hesperides and Eastern Deep located in the central part of the South Scotia Ridge show similar geological structure comprising two distinct sedimentary layers. The lower layer filled with fault breccia is considered to be formed with the expansion of the deeps. The upper layer is filled with pelagic sediments which implies this layer is formed after the spreading of the deeps has stopped. The south branch of the South Scotia Ridge is characterized by bigger width than the north branch. Topographical depression shown in the south branch is formed by many faults accompanied with the seafloor expansion of Powell basin.

• Proceedings of the Korea Contents Association Conference
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• 2010.05a
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• pp.633-634
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• 2010

축대칭 함몰지형 위를 진행하는 확장형 완경사 방정식의 해석해를 유도하였다. 변수분리법을 이용하여 지배방정식을 상미분방정식으로 만들었으며, 파속과 군속도로 표현되는 계수들은 Hunt(1979)의 근사식을 이용하여 양함수의 형태로 표현하였다. 마지막으로 Frobenius기법을 이용하여 확장형 완경사방정식의 해를 유도하였다.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.213-216
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• 2008

In this study, reflection coefficients of regular and random waves propagating over multi-arrayed trenchs are calculated respectively. When the row of trench is 3, the reflection coefficient of regular waves is more than 0.7 as maximum value. Similarly, when the row of trench is 3 and $d/L_1$ is 0.22, reflection coefficient of multi-directional random waves is more than 0.4 maximally.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.36-36
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• 2017

일반적으로 유역의 지형학적 특성을 나타내는 인자들은 유역면적, 유로연장, 유로경사 등 여러가지가 있다. Horton (1945)은 수계의 발달 형태에 기초한 하천의 차수를 이용하여 분기비, 길이비, 면적비, 하천 밀도 등 지형학적인 매개변수로 제시하였다. 유역 지형학적 매개변수는 Horton이 제시한 유역내 하도망의 지형학적인 구성에 대한 특성을 반영하는 것으로 유출에 지배적인 영향을 미친다. 한강 유역 19개 하천의 27개 지점을 대상으로 유출 특성과 지형학적 특성의 상관 분석을 위하여 유역과 하천의 지형학적 특성을 Arc-Map을 이용하여 구하였다. 하천차수법칙에 의한 지형학적인 매개변수로 분기비, 길이비, 함몰도, 면적비를 산정하였고, 유역의 지형학적 인자는 유역면적, 유로연장, 유로경사, 형상계수, 단일형상계수, 세장률, 수계밀도, 수계빈도를 산정하였다. 수계의 연간 유출률은 실측 유출량과 강수량 자료를 이용하여 산정하였다. 각각의 지형학적 특성인자에 대한 상관 매트릭스를 분석하고 그 상관특성을 분석하였다. 특히 지형학적 매개변수와 지형학적 요소와 연간 유출률과의 상관관계식을 제시하였다.