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Article

Physical Mechanism for Seabed Scouring around a Breakwater—A Case Study in Mailiao Port

1
Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
2
Department of Harbor & River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2022, 10(10), 1386; https://doi.org/10.3390/jmse10101386
Submission received: 17 August 2022 / Revised: 18 September 2022 / Accepted: 23 September 2022 / Published: 27 September 2022
(This article belongs to the Special Issue Breakwater Behaviour)

Abstract

:
According to a field survey in 2012, the bathymetry near Mailiao Port, located in central Taiwan’s west coast, has a scouring hole that extends approximately 500 m × 100 m with a maximum scour depth of 26 m (eroded from its design depth −22 m to −48 m). To investigate the scour mechanism near the breakwater head and prevent the breakwater from collapsing, this study conducts comprehensive analysis by analyzing field observed data, performing hydraulic model tests, and conducting numerical modeling for the area near the Mailiao Port. The results show that the current plays an important role in the scour process. The physical model tests and numerical simulations both can reproduce the scour phenomenon of the study site. By analyzing field observed data we validated through physical and numerical models. This study concludes that the current caused by the ebb and flood tide, as well as the steep and shallow seabed topography, together comprise the seabed scour mechanism near the Mailiao Port breakwater head.

1. Introduction

The breakwater is a coastal structure that divides the inner and outer parts of the port. Its main function is preventing the erosion of waves and drifting sand, maintaining the calmness of the port, and ensuring the safe entry and exit of ships. The mechanism of flow driven by waves and tides may scour the seabed near maritime structures such as breakwaters and seawalls and may damage or topple these structures. Take the Mailiao Port on central Taiwan’s west coast as an example. The original design depth at the toe of the West Breakwater head was approximately −22 m. According to a bathymetry survey in 2012, a scour hole with an area of approximately 500 m × 100 m formed at the seabed near the West Breakwater head, and the inmost depth is −48 m, and the erosion depth has reached 26 m.
Severe erosion of the seabed near the breakwater head may cause the breakwater structure to be damaged. However, the cause and mechanism of the erosion are still unclear. Therefore, observation, experiment, and simulation are needed for investigation to find the solutions to prevent or mitigate the damages. This study conducts comprehensive analysis by collecting and analyzing field data, performing physical hydraulic model tests, and conducting numerical modeling for the area near the Mailiao Port to investigate the scour mechanism near the breakwater head. Research regarding the breakwater fluid-structure interaction, hydro-dynamic modeling, and scouring are discussed as follows.

1.1. Scour around Breakwater

(1) 
General breakwater
Sato and Irie [1] investigated the relationship between the toe scour depth and wave data of the breakwater at Koshima Port and discovered that the farther the wave deviates from the normal incidence angle, the greater the topographic change and the greater the scour depth is. In addition, it is pointed out from the test results that the scour depth can be reduced by increasing the roughness of the breakwater surface. Xie [2], Irie, and Nadaoka [3], Sumer and Fredsøe [4], Fredsøe and Sumer [5], and Sumer and Fredsøe [6] performed a series of experimental studies but only for the standing wave case of total wave reflection. The scour profile is consistent with the characteristics of the nodal and anti-nodal positions of the standing wave. Irie and Nadaoka [3] performed experiments and classified scour type in front of the breakwater head as L-type and N-type according to the locations where the deposition occurs.
Xie [2] and Sumer and Fredsøe [6] proposed a regression empirical formula for the relationship between the scour depth and the relative water depth in front of the breakwater based on the experimental results. In the case of non-breaking waves, Herbich and Ko [7] derived the theoretical formula for toe scour from the balance point of view of the force on sand grains. Hales [8] used a field example to statistically analyze the length of armor required for the toe of the breakwater.
Eckert [9] concluded that when the downwash flow occurred in front of the breakwater, the maximum flow force acts on the toe, and the minimum length of the armor is designed accordingly, but the result is not applicable when the water depth of the breakwater toe is less than twice the wave height, and the reflectivity in front of the breakwater is greater than 0.25 or the slope of the embankment is greater than one-third. Sato et al. [1] concluded from the experimental results that the wave characteristics and reflectivity in front of the breakwater are the main factors affecting the scour at the breakwater toe. It was also found that the water flow around the structure is one of the factors affecting the scour. Sumer and Fredsøe [6] and Sumer et al. [10] revised the empirical formula of Xie [2] for the case of vertical breakwater to be used in cases of sloping face breakwater, and the empirical formula still takes the relative water depth in front of the breakwater as the parameter. However, the above literature did not consider the factor that the wave may cause downwash flow on the breakwater surface due to breaking waves.
Lin and Jeng [11] used the Coulomb-damping porous bed to analyze the liquefaction of breakwaters under the wave field and found that the most influential region is the wavelength relative to water depth 0~0.3. Burcharth et al. [12] performed experiments to explore the influence of different breakwater base materials on the structural stability and tried to use the type of combined base material to slow down the scouring process. Gislason et al. (2009) used the shear stress ω–ϵ (SST) model to investigate the scour phenomenon under the condition that the wave field degenerates to standing waves. They found that when the wavelength/depth ratio is less than 0.05, the ratio of scour depth and wave height will be greater than 1.
(2) 
Vertical-wall breakwater
Much research, such as that by Sumer and Fredsøe [4], Fredsøe and Sumer [5], Sumer and Fredsøe [6], Sumer et al. [10], Myrhaug et al. [13], Sumer et al. [14], Lee and Mizutani [15], and Myrhaug and Ong [16] has conducted experimental investigations regarding the characteristics and mechanisms of topographical erosion near the vertical-wall breakwater head. These investigations were performed at sites with and without breakwater head foundation protection and wave current interaction. However, although these researchers did not investigate deep water areas, their results were references for this study. The aforesaid research findings are summarized as follows:
A 
Effect of wave-induced current on breakwater head erosion
Sumer and Fredsøe [4] and Sumer et al. [14] discovered that when the wave incidence direction is normal to the breakwater, the vortex formed at the breakwater side is the dominant mechanism for erosion. The relationship between the wave characteristics and breakwater size can be expressed as a Keulegan–Carpenter (KC) parameter (=UmT/B). When KC < 1, no obvious vortex flow occurs in the current field; when 1 < KC < 12, the current field forms a wake vortex behind the breakwater; when KC > 12, in addition to the wake vortex behind the breakwater, a horseshoe vortex occurs in front of the breakwater. If the wave-induced current acts simultaneously (in the same direction), then the scour depth is correlated with the wave-induced current divided by the bottom current velocity induced by the waves. When the shields parameter exceeds the threshold, the relative scour depth of the bottom (ratio of scour depth to breakwater width) increases with the KC number; when only the wave-induced current velocity is effective, the scour depth increases.
B 
Wave action on breakwater head erosion with foundation protection
Gokce et al. [17], Myrhaug and Ong [13], Myrhaug et al. [16], and Shoji and Isao [18] discovered that when the wave incidence direction is normal to the breakwater, the scour is severe. When the bottom flow induced by waves is parallel to the breakwater, a scour channel may form along the breakwater toe. The amplitude of the scour can be reduced if the foundation protection of the bottom is present. When no foundation protection is present at the breakwater head, the ratio of the foundation protection width to the breakwater width is Lp/D = 0, and the scour depth increases significantly. When the ratio of the foundation protection width to the breakwater body width is Lp/D > 3.6, the scour depth amplitude at the breakwater head can be reduced. Similar results were verified in the case of irregular waves.
C 
Breakwater head erosion of wave action on vertical breakwater and sloping mount breakwater
Sumer et al. [10] found that wave steepness, the water depth in front of a breakwater, and breakwater slope critically influence the scour process by discovering that the sloping rubble mount breakwater reduces the amount of erosion in front of a breakwater more than an vertical breakwater.

1.2. Applying the Hydrodynamic Model to Calculate Wave and Current Field

Dentale et al. [19] built the breakwater protection model based on the configuration of hydraulic model testing and analyzed the reflection, transmission, run-up, overtopping, and surf of wave current on the wave trap as well as the stability of the structural foundation. Lai et al. [20] used this model to calculate the wave transformation, flow-field, and turbulence characteristics of an impervious and porous bed. The results showed that direct three-dimensional simulations can resolve the wave and velocity profile more completely. Due to the friction and infiltration of porous layers, wave energy dissipates between the surf and swash zones, and flow-field and turbulence characteristics are distinct. Acharya [21] used the turbulence model of FLOW-3D to simulate a series of spur-breakwater-plane bottom scour mechanisms and quantitatively analyzed longitudinal, lateral, and vertical plane turbulent current fields around the breakwater. A spatial variation in wave height and water level is found between the submerged breakwater and the vertical seawall, and the maximum wave height occurs at the location of the antinodes. Hirt and Sicilian [22] found that spatial variation of water set up behind the submerged breakwater is similar to that of the wave height. Lin et al. [23] use FLOW3D to perform fixed-bed simulation for the sea area near Mailiao Port and investigate the relationships between seabed velocity, excess shear stress, and the scour area.

2. Study Area

Mailiao Port of Mailiao Industrial Park is located at the south side of the Jhuoshuei River mouth (see Figure 1). Since the Port was constructed in 1994, deposition has been occurring at the north side of the north breakwater. West breakwater III construction began in March 1998 and continued until September 2000. Due to the extension of breakwater, tidal effects, and sand source from the Jhuoshuei River, the seabed topography at the toe of the Western Breakwater of Mailiao Port had dramatically changed. The designed water depth of the Western Breakwater in Mailiao Port in 2000 was −22 m. A scour hole with an area of approximately 500 m × 300 m at the west side of the breakwater head formed in 2001. Since then, the scour area and volume has been increasing throughout the years, and the erosion depth reached the maximum in 2007 (see Figure 2). However, the scour area and volume started to decrease after 2007.

3. Methods

3.1. Field Data Collocation and Analysis

The collection and analysis of field measured data is the basis for understanding the hydrodynamic characteristics of the sea area and the changes of seabed topography in the study area. The statistical analysis of historical sea state, meteorological, and geomorphological data is used as a reference for establishing numerical models for modeling waves, current, and seabed topography change, as well as the basis for setting the hydraulic model test. Since 1991, Tainan Hydraulics Laboratory (THL) has been conducting long-term meteorological, sea state, hydrological, and topographic surveys in the sea area of the Mailiao Industrial Park in Yunlin County. The locations of THL’s marine and meteorological observation stations are shown in Figure 3. This study takes the Mailiao Port as the study area and conducts statistical analysis on the meteorological, sea state, and topographic data in Yunlin County sea area.

3.2. Hydraulic Model Test

3.2.1. Wave Basin

The hydraulic test was carried out in the wave basin of Department of Engineering Science and Ocean Engineering, National Taiwan University. The wave basin is 40 m long, 25 m wide, and 1 m deep. The initial mobile-bed topography in the physical model is setup based on the topography surveyed in 1989, when the West Breakwater finished its construction. Arrays of wave gauges and velocimeters are setup up at west side of the West Breakwater in the wave basin, as shown in Figure 4.

3.2.2. Model Scale

In general, to represent prototype physical mechanisms, the model tests must meet following requirements: geometric similarity, kinematic similarity, and dynamic similarity. Sometime when the laboratory does not have sufficient space and the water depth of the wave basin is limited, a distorted scale model is required. The factors that cause the change of wave height are water depth, refraction, diffraction, and reflection. The former two are the influence of water depth change on the wave, and the latter two are the deformation of the wave when it encounters the obstruction of the structure. The abovementioned test scenarios and corresponding physical model scale ratios are listed in Table 1. The selected test scenarios are shown in Table 2. Two distorted scale ratios are implemented, one is λ h / λ L = 1, where λ L = 1/100, and another is λ h / λ L = 3, where λ L = 1/210, λ h = 1/70. In scenarios use λ h / λ L = 1, sand with D50 = 0.28 mm is used. For scenarios use λ h / λ L = 3, D50 = 0.15 mm is used. The use λ h / λ L = 3 and smaller grain size sand is to reduce the viscosity effect due to the downscaling of the physical model in order to investigate whether it affects the test results.

3.2.3. Boundary Conditions

(1)
Tidal Boundary Conditions
The tidal boundary conditions are set as follows. For monsoon waves, the design average tide level is set as +0.35 m; for typhoon waves, the design average high tide level is set as +2.10 m.
(2)
Wave Boundary Conditions
As for the wave boundary conditions, the test uses the northward wave from January 2001 to 2013 at Sihu Station (THL2B), in which the significance wave height (H1/3) is 2.65 m, and significant wave period (T1/3) is 6.32 s. The typhoon wave conditions were calculated using the northward wave conditions of the 100-year return period in the sea at Mailiao Port. The significant wave height is set as H1/3 = 6.4 m, and the significant wave period is T1/3 = 10.6 s.

3.3. Numerical Simulation

In this study, simulations of 3D flow near the breakwater were performed using FLOW-3D V10.1. This software includes a CFD code that can be used to solve fully 3D transient Navier–Stokes equations by using a finite-volume finite-difference method in a fixed Eulerian grid. This code was chosen for this study because of its flexibility and functionality in the scour potential model. The theoretical basis of FLOW-3D is well documented in Lin et al. [23]. This study used the RNG turbulent flow model, with default critical shields parameter of 0.05 and a default critical packing fraction value of 0.64.

3.3.1. Model Domain

The three-dimensional numerical mobile-bed simulation of the wave field is based on the calculation range of the sea area near the West Breakwater head (see Figure 5). To compare the numerical modeling results with the laboratory model test results, the modeling range is set to 1.5 km × 2.5 km. The northeast corner is the sheltered area for wave-making and diversion, and the bottom boundary is set up based on the topographic survey data of the study area. According to the grid independence test results, the north–south direction grid (Ay) of the wave field is set to 1/20 wavelength, the east–west direction grid (Ax) is set to 1/10 wavelength, and the vertical grid (Az) is set to 1/10 of the wave height.

3.3.2. Wave Field Modeling Input

In order to understand the wave and current field caused by waves close to the breakwater head, the calculation range is narrowed by refining the grids near the breakwater head. The input parameters of numerical model are shown in Table 3. The boundary of the incident wave is from the northern sea area, and the modeling scenario is the 50-year return period typhoon.

3.3.3. Current Field Modeling Input

Based on the survey conducted in 2014, the tide level records of the current meter ML station in the sea area of Mailiao Industrial Port are used as the boundary water level condition in the numerical model to simulate the tidal current of the sea area near Mailiao Industrial Port.

4. Results

4.1. Field Data Analysis

4.1.1. Bathymetry Data Analysis

(1)
Erosion and deposition trend of the seabed
According to the bathymetry data of the Yunlin-Chiayi counties sea area, the topographical changes adjacent to the West Breakwater of Mailiao Port from 1993 to 2010 are shown in Figure 6. The north side of the Mailiao port is close to the Jhuoshuei River mouth. In general, the abundant sand source from Jhuoshuei River causes deposition at the north side of the West Breakwater. On the other hand, the drift sand from the south side of the port is blocked by the breakwater, which greatly reduces the deposition rate.
From 1993 to 1996, when the West Breakwaters II and III had not yet been constructed, the change of bathymetry ranged from −2 m to +2 m. The erosion of −8 m can be found in the southern half of the West Breakwater I, while the deposition of +4 m at the north side of the West Breakwater I indicates that the breakwater has blocked a certain amount of drifting sand. From 1996 to 1998, the erosion and deposition pattern is similar to the past 2 years, except that with the construction of the West Breakwater II accelerate the process. During 1996 to 1998, the deposition at the north side of West Breakwater II exceeded +10 m, whereas the erosion near the head of West Breakwater II reached −12 m.
From 1998 to 2000, the West Breakwater III continued to extend to the open sea on the southwest side of Mailiao Port, and more drifting sand is accumulated at the northern area of West Breakwater II, with an extent of 1.25 km × 2.3 km and elevation of +2~+10 m. The entrance of Mailiao Port is affected by the sand blocking effect of the West Breakwater, and the maximum erosion is about −12 m. The north side of West Breakwater III continues to be eroded to −12 m at maximum. From 2000 to 2002, the scour hole moved southward to the west side of the West Breakwater III, that is, the breakwater head, and the depth of the scour hole was deepened to −14 m. During this period, the north side of the West Breakwater showed a significant pattern of deposition. From 2002 to 2004, the erosion and deposition pattern are similar to the past 2 years, and the scour hole at the breakwater head moved further toward the southwest direction. From 2004 to 2005, the scour hole with depth of −12 m at the breakwater head was greatly expanded, while the deposition adjacent to the breakwater body was reduced to +2~+4 m.
The same repeating pattern of erosion and deposition has shown in the records from 2004 to 2005, 2005 to 2006, 2006 to 2007, and 2007 to 2008. From 2008 to 2009, the previously described erosion and deposition pattern had stopped. During the 2007~2008 period, the deposition had increased by +2~+12 m, and the erosion has increased by −0.5~−4 m. During the period of 2009~2010, the erosion and deposition distribution had recovered to the one as in the 1998~2000 period. That is, large-scale of deposition occurred at the north side of the West Breakwater, whereas the erosion occurred in the south side of the West Breakwater. However, at the breakwater head, the erosion occurred at the north side and deposition occurred at the south side. Based on the erosion and deposition analysis from 1998 to 2010, the north side of the West Breakwater showed a trend of deposition and reach +20 m at maximum. On the other hand, the west side and southwest side to the West Breakwater formed two scour holes with maximum erosion of −20 m.
(2)
Evolution of the Scour Hole
The West Breakwater and the South Breakwater were constructed in chronological order from 1984 to 1989. During the construction period, scouring occurred near the head of the breakwaters. Figure 7 shows the map of topographic contour near the head of the West Breakwater of Mailiao Port from 1980 to 1999, including −25 m, −30 m, −35 m, and −40 m bathymetry contours. Among them, the −35 m bathymetry contour is a closed circle (within the observation domain), which can be used to represent the scour hole with a water depth greater than −35 m (hereinafter referred to as −35 m scour hole). As shown in Figure 7, during 1991 and 1996, the West Breakwater had not been extended to its current location, and the −20 m bathymetry contour remained parallel to the coast.
In 1998, the construction of the West Breakwater II caused erosion near the breakwater head and the scour hole had deepened from −15 m to −25 m. In 2000, the extension of the West Breakwater III formed a −30 m deep scour hole near the breakwater head. In 2001, the −30 m scour hole in front of the breakwater head had expanded, and another −35 m scour hole also appeared at the southwest side of the breakwater head. The scouring trend continued after 2001. The scour hole continued to deepen and exceeded −40 m in 2003. Figure 8 shows the development of the scour hole near the breakwater head from 2001 to 2010. Figure 9 shows that the contour area, scour volume, and maximum scour depth of the −35 m scour hole have been increasing since 2001, and they all peaked in 2007 with value of 197,300 m2, 7,868,464 m3 and 47.45 m, respectively.
After 2007, the scour area started to shrink, but it still maintained a considerable range. The X-axis direction is about 264–293 m, and the Y-axis varies about 669–742 m, with the average scour depth between 36 and 40 m. It can be seen from Figure 7 that during 2002 to 2007, the −20 m bathymetry contours within 300 m of the north side of the breakwater were all eroded toward the shore. That is, there is a sand source from the Zhuoshui River mouth. It can be seen from the period during 2007 to 2008, the scour hole had been filled up due to deposition, and the trend continued after 2008. Since 2001, the scour cross- sectional area and scour volume of the 35 m scour hole in Mailiao Port continue to increase, and the erosion amount reached the maximum in 2007. After 2007, it started to decrease, and the scour hole was gradually filled up.
(3)
High resolution bathymetry data
The analysis described in the previous section uses large-scale topographic data in the Yunlin- Chiayi counties sea area. The survey time interval is about one year or more, and the spacing of survey line is wider. Because extreme wave events may occur within a year, the erosion and deposition may have occurred multiple times within a year, so it is not easy to comprehensively analyze the scour characteristics and mechanism within a year. This research collects 39 records of topographic data of breakwaters and waterways provided by the port management company of Mailiao Industrial Park from April 2007 to September 2012 for further exploring the seasonal topographic change due to erosion and deposition. Figure 10 shows the high-resolution depth contour near the head of the West Breakwater of Mailiao Port from 2007 to 2012, including −30 m, −35 m, and −40 m contour lines.
As can be seen in Figure 10, during 2007 to 2012, the −35 m scour hole near the head of the West Breakwater in different months did not change drastically. The different values are mainly due to the high density of survey lines measured in large-scale sea areas and the high accuracy in local areas. According to the water depth survey data provided by the port management company of Mailiao Industrial Park, a total of six measurement periods coincided with the issuance of typhoon warnings by the Central Weather Bureau, namely, Typhoon Wipha in September 2007, Typhoon Mitag in November, Typhoon Linfa in June 2009, Typhoon Molave in July, and Typhoon Parma in October. In terms of the typhoon paths, both Wipha and Krosa passed through the northeastern corner of Taiwan and crossed the Taiwan Strait.
Mitag passed through south of Taiwan and disappears into the Bashi Strait. Linfa goes northward along the Taiwan Strait from the western coast of the Philippines to China’s Fuchien Province. Molave and Parma passed through the south of Taiwan. After the typhoon passed, not all cases showed erosion or deepening of the scour hole. For example, after Typhoon Parma passed, the topographic changes show deposition, and the scour hole were filled and became smaller. Taking the Linfa Typhoon as an example, it has no significant impact, either on the topographical change or the scour hole size. However, Wipha Typhoon caused extensive erosion and increased the depth and erosion volume of the scour hole. The results show that individual typhoon does not necessarily cause erosion on the topography of the seabed adjacent to the West Breakwater. A trend can be observed from Figure 11. During the summer (from April to September), the erosion area and volume of the −35 m and −40 m scour holes gradually increased. On the other hand, during the winter (from October to next March), the scour area and volume of the scour hole gradually decreased. This deposition trend is due to the sand source provided by the Jhuoshuei River.

4.1.2. Current Characteristics of Six Major Ports

This study collects the historical current data of six ports including Keelung, Taipei, Taichung, Mailiao, Anping, and Kaohsiung up to 2008 and analyzes the probability of current velocity over 50 cm/s (approximately 1 knot). The results are shown in Figure 12.
According to the annual statistics data, the probability of current velocity over 1 knot at Mailiao Port is 36.6%, which is significantly greater than that in other ports (except for Taichung Port). During June and September, the probability even increases to 40%. In the environment with such high-speed currents, it can be explained that the main reason for the erosion near the breakwater head of Mailiao Port is due to ocean currents. In this study, we further calculated the probability distribution of current velocity in Mailiao ports from 2000 to 2010, including current velocity less than 0.5 m/s, 0.5~1.0 m/s, 1.0~1.5 m/s, and current velocity greater than 1.5 m/s, as shown in Figure 13.
The probability of current velocity over 1.0 m/s in Mailiao Port during 2000 and 2007 was less than 2%. However, after 2007, the probability increased to 2~8%. In general, waves play the major role of activating near-bed sediments and the movement of sediment is driven by ocean currents, tidal currents, and wind-driven currents. Figure 13 also shows that currents near the Mailiao Port maintain a high velocity most of the time. As a result, although the water depth near the breakwater is over −20 m, and serious erosion still occurs, especially at the breakwater head. This reflects the erosion at the breakwater head is mainly caused by the current.

4.1.3. Relationship between Current Energy and Erosion

Different flow directions cause different sand drifting directions, and the long-term net drifting amount determines the erosion and deposition characteristics. Since there is no long-term sand drift observation data in the area near the West Breakwater of Mailiao Port, this study also collects and analyzes the current characteristics of the YLCW station in the Mailiao sea area and accumulates the net energy of currents for each month. Correlation analysis was carried out on the topographic data of 30 breakwater heads surveyed from April 2007 to September 2011.
(1)
Calculation of the current energy
To investigate the relationship between the current energy and the scour phenomenon, the energy of current is calculated based on hourly current data in winter (January) and summer (August) from 2000 to 2010 at Mailiao Port YLCW station. The current velocity and vector diagram is shown in Figure 14.
Because the current with a velocity less than 0.5 m/s has little effect on the topography, only the velocity greater than 0.5 m/s is selected for the analysis in this study. Additionally, the current with a flow velocity greater than 0.5 m/s is divided into the north–south and east–west components. The square of the current velocity is defined as the unit current energy (hereinafter referred to as the current energy, i.e., E i V i 2 ). Convert the current velocity components into the current energy components in the south–north and east-west directions, then accumulated the energy in the north-south and east–west directions by hours, and then the energy in north–south and east–west directions can be calculated. An example of monthly net current energy is calculated as follows:
North–South direction: E N S i 31 V i N 2 V i S 2 = + 535.17   (+ denotes north)
East–West directions: E N S i 31 V i E 2 V i W 2 = + 20.93   (+ denotes east)
Based on the above-mentioned approach, the monthly net current energy was calculated from the hourly ocean current data. Figure 15 is an example of cumulated current energy in May 2007, which shows that northward and southward current have significant cumulated energy. The eastward and westward current, on the contrary, have less cumulated energy. Data from 2000 to 2010 at the Mailiao Port YLCW station is collected for calculating long-term the cumulated current energy as shown in Figure 16. Note that the blue line is the southward and northward directions, and the red line is the eastward and westward directions. The monthly net current energy shows regularity, and the northward current energy gradually increases during summer; on the contrary, during winter, the southward current energy gradually increases. Among them, the monthly net current energy in the eastward and westward directions is relatively small, so it is not included in the analysis.
(2)
The seasonal trend of current energy and erosion
From the above analysis, we can obtain the net current energy of the Mailiao sea area in different months or seasons. Having the topographic data near the West Breakwater surveyed by the Mailiao Port Administration Corp. from April 2007 to September 2011, the current data during the same period are selected for analyzing the correlation and comparison with the topographic data. Figure 17 is an example of the erosion and deposition changes (from May to July and from August to September in 2007), along with the cumulative distribution of current energy. It is observed that the net current energy in summer is northward. When the northward sea current passes through the breakwater head, eddies are generated around the breakwater head, which increases the current velocity on the west and northwest sides of the breakwater head, causing the erosion at downstream side of the breakwater head (the north side of the breakwater head).
Figure 18 is an example of the erosion and deposition changes (from October to November 2009, and form November 2009 to January 2010), along with the accumulated current energy. It is observed that the net current energy in summer is southward. When the southward current passes through the breakwater head, eddies are generated around the breakwater head, which increases the current velocity on the west and southwest sides of the breakwater head, causing the erosion at downstream side of the breakwater head (the south side of the breakwater head).
At the same time, the southward current also pushes the sand at the mouth of the Jhuoshuei River to the south and is blocked by the West Breakwater and deposited at the north side of the West Breakwater head. From the above two examples in summer and winter, it can be preliminarily concluded that the erosion of the seabed near the breakwater is directly related to the seasonal changes of the current.
The data of all the −35 m scour hole at the breakwater head from 2007 April to 2011 September were compared with the cumulative current energy during the same period, as shown in Figure 19. The result shows that the net current energy in summer is northward (the main flow is northward), and the scour hole is at the north side of the breakwater head, but the south side of the breakwater head is a deeper water area (the navigation channel), and there is no sediment source to refill the scour hole to the north, resulting in the −35 m scour hole continuing to erode. In winter, the net current energy is southward (main flow is southward). With the drift sand from the mouth of the Jhuoshuei River at the north side of the breakwater, the scour hole will be backfilled during the winter. This seasonal pattern goes on and on, forming a recurrent phenomenon.

4.2. Hydraulic Test of Wave Field

4.2.1. Monsoon Waves

(1)
Wave field and current field
Under the northward monsoon wave conditions, the water level changes near the breakwater head are calculated. Under the action of monsoon waves, the wave height and period are relatively small, and the phenomenon of wave shoaling, and refraction is not obvious. Figure 20 and Figure 21 show that under the monsoon wave conditions, a depth of z = −15 cm has a greater velocity in the v-direction due to the incidence of northward waves. The u-direction current velocity is concentrated in the northwest of the breakwater head because the reflected oblique incident waves have a large -u velocity. It is shown that there is a southwestward current driven by the oblique incident wave, and the w-direction current velocity is greater in the reflection concentration area at the northwest side of the breakwater head. Figure 22 shows that the changes of the plane velocity and total velocity of the z = −10 cm layer. The velocity vectors of each measuring point of plane velocity are consistent in magnitude and direction.
(2)
Topographic changes
The topographic changes near the breakwater head are measured with 200 wave periods (about 126 s) each time the Northward monsoon wave acts. The scale of the model is equal to 1/100, the results of erosion and deposition after 200 wave periods, the results after 400 wave periods compared with the original topography, and the results after 600 wave periods are shown in Figure 23. The results show that the topographic changes are insignificant under the action of monsoon waves, and there is only slight deposition at the back of the breakwater head, and the range moves slightly toward the channel as the waves continue to act. In addition, except for slight erosion in the shallow water depth at the north side of the breakwater, most of the other areas are stable. The water depth at the head of the breakwater is about 19 m.

4.2.2. Typhoon Waves

(1)
Wave and current field
In Figure 24, the velocity components in each direction of each measuring point still show periodic changes in the selected time interval. It can be found that the typhoon wave conditions are quite close to shallow water waves, so the horizontal velocity difference between z = −15 cm and z = −10 cm is not significant and is symmetrical, and the velocity in the diffraction zone behind the breakwater is significantly smaller. The u-direction current velocity is greater in the repetitive wave area in front of the breakwater, the v-direction velocity is greater in the repeated wave action area at the head of the breakwater and the offshore area, and the w-direction velocity is still decreasing along the water depth direction.
Figure 25 shows the measured U from t = 26~27.08 s at z = −15, z = −10 and z = −8. It can be found that the current field at t = 26 s and t = 27.08 s are quite similar, which shows a periodic pattern and follows the cyclical trend of the northward and southward incident waves. In the process of wave advancing, the wave crest line is roughly consistent; that is, most of the measuring points in the east–west direction have the same flow direction.
If comparing Figure 25, it is found that the plane current field and the total current velocity distribution in the two water layers are roughly consistent. In the model test, the current velocity near the breakwater head is measured in more detail. Figure 26 shows that the current velocity changes, the position of the maximum current velocity moves from the north of the breakwater head to the breakwater surface with the northward incident waves and then follows the breakwater line. It moves southwest (t = 26.20 s) and then gradually divides into two parts (t = 26.24 s).
The distance between the two is about half a wavelength, so it can be inferred that one is a peak and the other is a trough. In the selected measurement time, the spatial distribution of the maximum current velocity U of each water layer is drawn as shown in Figure 27. It can be seen from the figures that the overall trend is roughly the same, but the upper layer velocity is larger. In addition to the large current velocity, there is an area with high current velocity in the z = −15 cm water layer on the west side of the breakwater head at x = −0.5~−1 m, and there is also a large current velocity area in the z = −8 cm water layer in the southwest corner of the breakwater head.
(2)
Topographic changes
Under the condition of the typhoon 1 wave, the model sand is glass sand after sieving and washing, the specific gravity is 2.651, the median particle size D50 = 0.28 mm, and the northward typhoon wave acts with 200 wave periods (about 212 s) as a cycle for the breakwater. For the measurement of topographic change near the head, the scale of the horizontal direction and water depth of the model is equal to 1/100, and the time scale is 1/10. The action of 200 wave periods is approximately equal to 35 min of typhoon wave action onsite. The results of erosion and deposition are shown in the Figure 28a–c. The results show that after 200 wave periods of typhoon waves acted on the breakwater, there was a little deposition behind the breakwater, while the outer boundary of the measurement area was slightly eroded. In addition to the slight erosion, there is a slight erosion phenomenon at x = −150 m, 150~200 m from the head of the breakwater. After 600 wave periods, the erosion area expands slightly and moves towards the head of the breakwater. Slight erosion also occurs at y = 150~200 m, but overall, the topographic scour and deposition changes only a little, and the breakwater foundation is stable.
In all model configurations with different ratios of 3, the model sand is re-laid as fine sand after sieving and washing, the specific gravity is 2.5, and the median particle size is D50 = 0.15 mm. Here, the wave conditions of typhoon 2 are carried out, the water depth scale ( λ h ) is 1/70, the horizontal scale ( λ L ) is 1/210, the incident wave period is 1.267 s, the wave height is 9.12 cm, and the test water depth is 60 cm to measure topographic change due to typhoon wave action. The test waves action of 200 wave periods (about 253 s) is approximately equal to the typhoon wave action of 106 min in the field. The measured erosion results are shown in Figure 28d–f. After 200 wave periods of typhoon waves acted on the typhoon, there was deposition behind the breakwater, while erosion occurred between the x-coordinate −100~−200 m and the y-coordinate −120~−230 m, and the deposition remained behind the breakwater after 400 wave periods. The above erosion area expands to the y-coordinate −30 m and the depth becomes slightly larger. After 600 wave periods, the erosion area continues to expand and moves to the direction of the breakwater head. In general, the breakwater is stable.
In the distorted scale model, it is found that the influence of waves on the topographic sand drifting in the measurement area is still insufficient. Therefore, it is considered to reduce the water level to increase the driving force on the bottom sand. For the test carried out under the wave conditions of typhoon 3, the water level was 52.1 cm, the period was 1.06 s, the wave height was 9 cm. The measurement is performed after 200 wave periods (about 212 s), which is approximately equal to the 89 min of onsite typhoon waves. The results of erosion and deposition are shown in Figure 28g. In terms of wave conditions, the difference is that the wave height is increased to improve the sharpness of the wave. The results show that there is still slight deposition behind the breakwater, and slight erosion occurs in the shallow water depth of about 150 m in the north of the breakwater. Most of the other areas are stable.
For the test carried out under the wave conditions of typhoon 4, the water level was 52.1 cm, the period was 1.267 s, the wave height was 11.38 cm, and the wave was measured after 200 wave periods. The results of erosion and deposition are shown in Figure 28h. The difference is that the wave height is increased, and the water level is lowered to improve the ability to activate sand particles. The results show that there is slight deposition on the back side of the breakwater head, and slight erosion occurs in the shallow water depth of about 150 m in the north of the breakwater. Another obvious erosion occurs in the breakwater. The head extends out about 200 m, and the rest are stable.
The experimental results show that after the northward typhoon wave acts on the three breakwater breakwaters in the west of Mailiao, erosion occurs in the area on the southwest side of the breakwater head, and the trend is consistent with the current condition. The sand drifting behavior of waves on the nearshore mostly plays the role of initiating the sediment, and the sediment transport behavior is caused by ocean currents, including tidal currents, wind-driven currents, or nearshore currents caused by waves, while currents are deep water drifting sand. The main driving force is transmitted, so the phenomenon of serious erosion still occurs on the water depth of the breakwater head above −19 m. It is speculated that the possibility of eddy current is high, and the joint action of tidal current and wave will be the focus of follow-up research.

4.3. Hydraulic Test of Current Field

4.3.1. Current Field

The test results show that the southward tidal current acts on the three breakwaters in the west of Mailiao and is affected by the topography in the area at the north side of the breakwater head, and the flow direction turns to south and southwest along the bathymetry contour. The current velocity at the location is relatively stable. The average current velocity at each point at z = −10 cm z = −15 cm are shown in Figure 29a. The current adjacent to the breakwater head is affected by the deep-water caisson breakwater, resulting in a southwestward contraction flow. Therefore, the measurement points near the breakwater head have relatively large westward velocity. The northward flow test results show that the area adjacent to the head of the three breakwaters is affected by the structures and topography, and the flow direction turns to the north along the bathymetry contour. The south side of the breakwater has a gentle slope due to channel dredging, and the flow rate is generally stable adjacent to the head of the breakwater. The current velocity increases due to the blocking of the breakwater, and the current velocity decreases due to the shielding effect on the northeast side of the breakwater. As shown in Figure 29b, the current field of the area adjacent to the breakwater head was affected by the deep-water caisson breakwater and produced a northwestward flow. Therefore, the west side of the breakwater head had a large westward current velocity.

4.3.2. Topographic Changes

The topographic change near the breakwater head were measured after 1, 2, and 3 h durations. The results of scour and deposition are shown in Figure 30a–c. After one hour of current action, the area near the inlet is slightly eroded, and the flow direction in front of the breakwater turns to the southwest due to the blocking effect of the topography and the breakwater. In the offshore area, alternate pattern of scour and deposition is observed. In general, the breakwater toe is stable, and only part of the pebbles near the breakwater head are displaced. After 2 h of current action, the area near the inlet continued to erode, and the erosion area on the west side of the breakwater head gradually extended to the south, while the original deposition area in the offshore area was reduced. The erosion area extends to the southwest side of the breakwater head, about 50~100 m from the west to the southwest of the breakwater head, which is consistent with the surveyed field data.
After the northward flow acts for 1, 2, and 3 h, respectively, the topographic changes near the breakwater head are measured. Figure 30d–f shows that after one hour of current action, there was slight deposition in the southeast of the breakwater, while there was slight erosion in the south of the breakwater head. After 2 h of current action, there was slight deposition in the southeast of the breakwater while there was slight erosion in the south and south-southwest side of the breakwater head. After 3 h of current action, a scour area developed at 100~150 m south of the breakwater heads.

4.4. Numerical Simulation of Wave Field

4.4.1. Water Surface Elevation

Figure 31 show the water surface caused by the incident wave after 45th and 80th wave periods near Mailiao Port. The incident wave from the north is blocked by the breakwater. The reflected waves overlap each other to form a short-peak wave field with complex water surface. The diffracted waves enter the shielded area at the south side of the West Breakwater, and the wave diffraction forms the fluctuation of the point wave source at the breakwater head. It is found that the breakwater has a good shielding effect on the incident waves from the north.

4.4.2. Wave-Induced Current Field

To understand whether the hydrodynamic behavior of extreme waves passing through the breakwater will lead to substantial changes in the seabed topography near the breakwater head, it is necessary to further analyze the current velocity of the seabed from the numerical calculation results of the wave field. The simulation result is shown in Figure 32.
Figure 32 shows the variation of the velocity u in the x-direction near the seabed when the 80th wave periods enter the simulation domain. Figure 33 shows the change of the seabed velocity and elevation in the scour area. The bottom velocity is between 0.57 m/s and 1.51 m/s. The seabed elevation is approximately between −20.32 m and −20.45 m.
The time series of the bottom velocity in the scour area shows that the wave field in this area is unstable, and it is positively correlated with the change of the erosion sequence; that is, when the erosion curve tends to be flat, the bottom velocity decreases relatively. As shown in Figure 34, the change of current velocity induced by the wave field is analyzed, showing that the westward current velocity u is between −1.41 m/s and 0.55 m/s, the southward current velocity v is between −1.47 m/s and 0.75 m/s, and the vertical current velocity is between −1.47 m/s and 0.75 m/s. The current velocity w was between −0.43 m/s and 0.53 m/s.
Among them, the current velocity u is negative in layers from −20.5 m (near the seabed) to −1.5 m (the water surface). It can be judged that the advancing wave train is caused by the shielding effect of the breakwater, causing the contraction of the flow and direct the flow into the scour area at the west side of the breakwater head.

4.4.3. Topographic Change

The net change in bed elevation is approximately 0.05 mm for simulation time between 510 s and 840 s, as shown in Figure 35.

4.5. Numerical Simulation of Current Field

4.5.1. Current Field

The sea area at the north side of Mailiao Port is set as the upper boundary of the simulation domain, the initial velocity is set to 1.0 m/s, and the time series of the flow vector distribution as shown in Figure 36a. Similarly, the sea area at the south side of Mailiao Port is set as the lower boundary of the simulation domain, the initial velocity is set to 1.0 m/s, and the time series of the flow vector distribution as shown in Figure 36b. The simulation also shows that the northward current is blocked by the West Breakwater structure, so the diffracted flow along the breakwater produces eddy currents in the sheltered area at the north side of the breakwater. Similarly, the southward flow is blocked by the West Breakwater, so the diffracted flow along the head of the breakwater produces eddy currents in the sheltered area at the south side of the breakwater.

4.5.2. Current Velocity at Different Depths

The simulation results are observed at different depths. Figure 37a shows that the maximum u of the northward current occurred at depth of −15 m, where the maximum velocity is −3 m/s. Figure 37b shows that the maximum v of the southward current occurred at depth of −15 m, where the maximum velocity is −2.2 m/s.

4.5.3. Tidal Effect on the Current Field

The numerical model uses the tidal level recorded in the sea area of Mailiao Port as the boundary condition and simulate the flow in an area of 12 km × 16 km × 50 km. Then a smaller region with area of 800 m × 800 m × 50 m (Figure 38) is modeled using the results from previous simulation as its boundary condition. The results are shown in Figure 39.
The current field conditions of various tidal intervals are discussed as follows.
(1)
At Low Tide Stage
The current field at low tide level forms a low-velocity area in the sea area outside the Mailiao Port, and the uniform flow vector is northward, indicating that the tide has begun to turn and enter the high tide stage.
(2)
At Flood Tide Stage
The main tidal current in the high tide stage of this sea area is northward. A belt-shaped area with high current velocity extends from the West Breakwater head to the north. The current velocity in this area is greater than 1.25 m/s. The east–west width is 1.5~2 km. Affected by the shape of the breakwater, the flow direction at the breakwater head is from northwest to north–northwest. A clockwise rotating vortex is generated at the north side of the West Breakwater.
(3)
At High Tide Stage
At high tide stage the tide level has begun to decline slowly, and turn into the low tide stage, and a weak counterclockwise rotating eddy current is generated in the area sheltered by the south side of the breakwater.
(4)
At Ebb Tide Stage
After the low tide stage, the overall flow direction turned from north to south, and the area with high current velocity moved south from the northern boundary and was stable in the west to northwest waters outside Mailiao Port. Close to the side of the west breakwater, there is a belt-shaped high-velocity system extending southward with the head of the breakwater, and the flow direction is between south and southeast.

4.5.4. Topographic Changes

The mobile-bed simulation results show that the rate of scour and deposition in the area is within ±5 mm/h. As shown in Figure 40 and Figure 41, the location of the scour area is at the southwest of the breakwater head, which roughly coincides with the field survey data.

5. Discussion

5.1. Field Data Analysis

According to the topographic data from 30 high-resolution surveys near the head of the West Breakwater from 2007 April to 2011 September (5 years of records), it is known that during the summer (from April to September), the area and volume of the −35 m scour hole gradually increased. During the winter (October to March), the area and volume of the scour hole gradually decreased. According to the historical current data, the probability of the current velocity over one knot at Mailiao Port is 36.6%, which is significantly higher than that of other ports in Taiwan (except for Taichung Port). As a result, although the water depth near the breakwater is over 20 m, severe erosion still occurs, especially at the head of the breakwater. When the current pass by the breakwater head, it changes direction and causes a velocity gradient. These phenomena cause the unbalanced sand drift and lead to the erosion of the breakwater head. The main current direction in the summer is northward, and the scour hole is at the north side of the breakwater head, but the south side of the breakwater head is a deeper water area, and the scour hole is replenished to the north without drift sand, resulting in increased erosion.
In the winter, the main current direction is southward, and the scour hole is formed at the south side of the breakwater head, but the alluvial sand from the mouth of the Jhuoshuei River is replenished at the north side of the breakwater head, and the drift sand from the south will gradually backfill the scour hole at the north side. According to the records, the construction of the West Breakwater must be suspended for 5 to 7 months during the northeast monsoon season every year. At the early stage of construction, the scour hole near the breakwater head has been formed because the deposition at Jhuoshuei River mouth is not significant and therefore cannot provide a sand source to backfill the scour hole. After the extension of the West Breakwater III is completed, the deposition at the north side of the breakwater becomes more significant. When the dominant current direction is southward in winter and northward in summer, the abovementioned seasonal changes near the head of the West Breakwater of Mailiao Port are formed. These phenomena indicate the ocean current is the main factor that cause the erosion near the breakwater head.

5.2. Hydraulic Test of Wave Field

The monsoon wave is incident on the breakwater obliquely, and the reflected wave causes large wave height and current velocity at the northwest of the head of the breakwater. There are larger -v and -u flow velocities at the west side of the breakwater head, indicating that there is a southwesterly current stream driven by waves obliquely incident on the breakwater. Under the action of monsoon waves, the topographic change is not noticeable, and there is only a little deposition at the back side of the breakwater head. Due to wave shoaling and refraction, the typhoon waves approach the normal incidence breakwater, forming repeating waves in front of the breakwater. The wave-induced current field near the breakwater head is relatively turbulent, forming a local short-peak wave pattern, which is divided into upper-left and lower-right halves by the extension of the breakwater line, which are caused by reflected waves and diffracted waves in front of the breakwater, respectively.
In the scenarios that use the undistorted model, there is slight deposition siltation behind the breakwater and slight erosion about 200 m from the head of the breakwater, but overall, the topographic change is not significant, the breakwater foundation is stable, and only a few pebbles are displaced. In the scenarios that use distorted model with increased wave height and lowered mean water level. The results showed that there is slight deposition on the rear side of the breakwater head, and more significant erosion was found about 200 m away from the breakwater head. About 150 m north from the breakwater also showed slight erosion. After the southward typhoon wave acts on the West Breakwater III, erosion occurs in the southwest side of the breakwater head, and the trend is consistent with the collected field data.

5.3. Hydraulic Test of Current Field

When the current direction is southward, the erosion occurs at west side of the breakwater head; when the current direction is northward, erosion occurs at 20~150 m south–southwest of the breakwater head, which is consistent with real physical phenomenon. Based on the test results, it is inferred that the local current field and eddy and breakwaters generate vertical current velocity to take up the sediment from the seabed, then carried and moved by current or waves, causing the scour at the West Breakwater head. Based on the test results, it can be inferred that tidal current and flow acceleration caused by the breakwater induced vertical velocity in this area and picked up the sediment from the seabed and then carried away by the longshore current. The results from hydraulic tests of different scenarios show that significant scour occurs under the act of current from different directions, which indicates the major cause of scouring is the current.

5.4. Numerical Simulation of Wave and Current Field

According to the numerical simulation results for the currents, it is shown that the breakwater head has the functions of shielding, diffracting and blocking the flood and ebb tides. Therefore, the accumulated current energy causes the westward banded offshore current and then mixes with the north–south tidal current to form a turbulent area with vertical and horizontal eddies. The results of the numerical simulation of the wave and current fields in the sea area near the Mailiao Port breakwater head show that the scour mechanism of the seabed near the breakwater head is composed of the wave-induced current field, the ebbs and flood tides, and the steep and shallow seabed topography. The advancing wave train in front of the breakwater is folded into the deep-water direction (westward) and forms rip currents, which mix with the southward advancing wave train and enhance the turbulence above the seabed boundary layer.

6. Conclusions

The breakwater is a maritime structure that is constructed to prevent the erosion of waves and drifting sand, maintain the calmness of the port, and ensure the safe entry and exit of ships. The scour mechanism near the breakwater head could endanger the structure safety and diminish the utility of the port. In central Taiwan’s Mailiao Port, a scour hole started to form after the West Breakwater III had finished construction, and years after, the scour hole had reached to its maximum depth of −26 m (from designed depth −22 m eroded to −58 m). To find a solution to mitigate the scour, this research conducted comprehensive analysis through field data analysis, hydraulic model tests, and numerical modeling. From field data analysis, we collected and analyzed long-term field data such as wave, current, and surveyed seafloor bathymetry. From hydraulic model test, we tested the scour mechanism using different wave and current conditions from designed monsoon and typhoon events and performed mobile-bed hydraulic tests. From numerical modeling, we used FLOW-3D to develop a 3D mobile-bed numerical model to simulate wave and current around the Mailiao West Breakwater under design wave and current boundary conditions. The results of the three approaches all confirmed that the scour mechanism is caused by the combination of the geometry of the breakwater, the sand source from the Jhuoshuei River, the seasonal change of sea current directions, the effects of tidal currents, and the wave directions. In general, the hydrodynamic energy accumulated by the advancing wave train in front of the breakwater, and the refracted rip current that moves toward the deep-sea area are mixed with the southbound advancing wave train and enhance the turbulence mechanism of the seabed boundary layer, causing the suspended load moving away from the scour area along with the tidal current. Because of the long-term lack of a sediment source, the erosion and siltation at the scour area is unbalanced, which continues to threaten the stability of the breakwater structure.

Author Contributions

Conceptualization, I.-F.T. and C.-H.H.; methodology, I.-F.T.; software, P.-H.Y.; validation, I.-F.T., C.-H.H., P.-H.Y. and T.-C.L.; formal analysis, P.-H.Y.; resources, I.-F.T.; data curation, T.-C.L.; writing—original draft preparation, C.-H.H.; writing—review and editing, T.-C.L.; visualization, C.-H.H.; project administration, I.-F.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Harbor and Marine Technology Center, Institute of Transportation, Ministry of Transportation and Communications, Taiwan. Project No.: MOTCIOT-104-H2DB005d.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Restrictions apply to the availability of these data. Data was obtained from Mai-liao Harbor Administration Corporation and are available with the permission of Mai-liao Harbor Administration Corporation.

Acknowledgments

This study was supported by Harbor and Marine Technology Center, Institute of Transportation, Ministry of Transportation and Communications, Taiwan, Project No. MOTCIOT-104-H2DB005d.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Mailiao Port in Central Taiwan.
Figure 1. Mailiao Port in Central Taiwan.
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Figure 2. The scour hole in front of Mailiao Port West Breakwater.
Figure 2. The scour hole in front of Mailiao Port West Breakwater.
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Figure 3. Location of tidal wave and current stations.
Figure 3. Location of tidal wave and current stations.
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Figure 4. The topography and measurement device setup in wave basin.
Figure 4. The topography and measurement device setup in wave basin.
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Figure 5. Model domain for numerical simulation.
Figure 5. Model domain for numerical simulation.
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Figure 6. The topographic change near Mailiao West Breakwater.
Figure 6. The topographic change near Mailiao West Breakwater.
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Figure 7. The topographic data near Mailiao West Breakwater.
Figure 7. The topographic data near Mailiao West Breakwater.
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Figure 8. The development of the scour hole near the West Breakwater.
Figure 8. The development of the scour hole near the West Breakwater.
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Figure 9. The scour area, volume, and depth of the −35 m scour hole.
Figure 9. The scour area, volume, and depth of the −35 m scour hole.
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Figure 10. High-resolution topographic data near the West Breakwater.
Figure 10. High-resolution topographic data near the West Breakwater.
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Figure 11. The area and volume of the −35 m and −40 m scour holes near the West Breakwater.
Figure 11. The area and volume of the −35 m and −40 m scour holes near the West Breakwater.
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Figure 12. The current velocity probability.
Figure 12. The current velocity probability.
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Figure 13. The current velocity of six major ports of Taiwan.
Figure 13. The current velocity of six major ports of Taiwan.
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Figure 14. Current velocity vector diagram (1-month data).
Figure 14. Current velocity vector diagram (1-month data).
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Figure 15. Cumulated energy for velocity > 0.5 m/s.
Figure 15. Cumulated energy for velocity > 0.5 m/s.
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Figure 16. Cumulated current energy in 11 consecutive years.
Figure 16. Cumulated current energy in 11 consecutive years.
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Figure 17. The cumulated energy at station YLCW and topographic change near the West Breakwater in summer (one-month data).
Figure 17. The cumulated energy at station YLCW and topographic change near the West Breakwater in summer (one-month data).
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Figure 18. The accumulated energy at station YLCW and topographic change near the West Breakwater in winter (one-month data).
Figure 18. The accumulated energy at station YLCW and topographic change near the West Breakwater in winter (one-month data).
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Figure 19. Scour volume and cumulative energy near the West Breakwater in 4 consecutive years.
Figure 19. Scour volume and cumulative energy near the West Breakwater in 4 consecutive years.
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Figure 20. Max u, v, w at west side of the West Breakwater (z = −15 m).
Figure 20. Max u, v, w at west side of the West Breakwater (z = −15 m).
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Figure 21. Max u, v, w at west side of the West Breakwater (z = −10 m).
Figure 21. Max u, v, w at west side of the West Breakwater (z = −10 m).
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Figure 22. U at west side of the West Breakwater under the action of monsoon waves (z = −15 m).
Figure 22. U at west side of the West Breakwater under the action of monsoon waves (z = −15 m).
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Figure 23. Topographic change under the action of monsoon waves.
Figure 23. Topographic change under the action of monsoon waves.
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Figure 24. Max u, v, w at west side of the West Breakwaters at z = −15 m.
Figure 24. Max u, v, w at west side of the West Breakwaters at z = −15 m.
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Figure 25. U at west side of West Breakwater under the action of typhoon waves (z = −15 m).
Figure 25. U at west side of West Breakwater under the action of typhoon waves (z = −15 m).
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Figure 26. U around the West Breakwater under the action of typhoon waves (z = −15 m).
Figure 26. U around the West Breakwater under the action of typhoon waves (z = −15 m).
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Figure 27. Max current velocity under the action of typhoon waves.
Figure 27. Max current velocity under the action of typhoon waves.
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Figure 28. Topographic change under typhoon 1 scenario.
Figure 28. Topographic change under typhoon 1 scenario.
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Figure 29. Current field at z = −10 and z = −15 under the action of current.
Figure 29. Current field at z = −10 and z = −15 under the action of current.
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Figure 30. Topographic change under 1, 2, 3 h action of current.
Figure 30. Topographic change under 1, 2, 3 h action of current.
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Figure 31. Water surface of simulated wave field.
Figure 31. Water surface of simulated wave field.
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Figure 32. The bottom u, v, w velocity field.
Figure 32. The bottom u, v, w velocity field.
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Figure 33. Bottom velocity and topographic change at the probe location.
Figure 33. Bottom velocity and topographic change at the probe location.
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Figure 34. Time series of u, v, w velocity.
Figure 34. Time series of u, v, w velocity.
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Figure 35. Topographic change at t = 510 s and 840 s.
Figure 35. Topographic change at t = 510 s and 840 s.
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Figure 36. Depth-averaged flow velocity vector under the action of southward and northward currents.
Figure 36. Depth-averaged flow velocity vector under the action of southward and northward currents.
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Figure 37. The u (a) and v (b) velocity fields under the action of southward current at z = −15 m.
Figure 37. The u (a) and v (b) velocity fields under the action of southward current at z = −15 m.
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Figure 38. Modeling domain with high resolution computation grids.
Figure 38. Modeling domain with high resolution computation grids.
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Figure 39. Depth-averaged flow velocity vector at low, flood, high, and ebb tide stages.
Figure 39. Depth-averaged flow velocity vector at low, flood, high, and ebb tide stages.
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Figure 40. Topographic changes at low and flood tide stages.
Figure 40. Topographic changes at low and flood tide stages.
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Figure 41. Topographic changes at high and ebb tide stages.
Figure 41. Topographic changes at high and ebb tide stages.
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Table 1. Distorted scale ratios of physical quantities for mobile-bed test from the literature.
Table 1. Distorted scale ratios of physical quantities for mobile-bed test from the literature.
Author(s)Derivation PrincipleNTNH
Goddet and Jaffary (1960)Bed Sediment Kinematic Similarity μ 1 / 2 μ
Valembois (1960)Suspended Sediment Kinematic Similarity μ 1 / 2 μ 4 / 5
Yalin (1963)Dimensional Analysis μ 1 / 2 μ
Fan and LeMehaute (1969)Bed Sediment Kinematic Similarity μ 1 / 2 μ
Noda (1972)Bed Sediment Kinematic Similarity μ 1 / 2 μ
Dalrymple and Thompson (1976) μ / ω Similarity μ 1 / 2 μ
Note: NT: wave period scale ratio; NH: wave height scale ratio; μ : vertical scale ratio.
Table 2. Test scenarios and corresponding scale ratios and grain size.
Table 2. Test scenarios and corresponding scale ratios and grain size.
Simulation
Scenario
Prototype (Model)
Wave
Direction
Wave
Height
Wave
Period
Tide
Elevation
Distorted Scale Ratio
λ L / λ H
Grain
Size
MonsoonSouthward2.65 m (2.65 cm)6.32 s (0.632 s)0.35 m (0.35 cm)10.25 mm
Typhoon1Southward6.4 m (6.40 cm)10.6 s (1.06 s)2.1 m (2.1 cm)10.25 mm
Typhoon 2Southward6.38 m (9.12 cm)10.6 s (1.267 s)3.0 m (3.0 cm)30.15 mm
Typhoon 3Southward6.30 m (9.00 cm)8.9 s (1.06 s)2.1 m (2.1 cm)30.15 mm
Typhoon 4Southward7.97 m (11.38 cm)10.6 s (1.267 s)2.1 m (2.1 cm)30.15 mm
Note. λ L = vertical scale; λ H = horizontal scale.
Table 3. FLOW-3D Model Input Parameters.
Table 3. FLOW-3D Model Input Parameters.
ScenarioWave Height (H)Wave Period (T)Wave DirectionSimulation Time
50-year Return Period Typhoon at Mailiao6.4 m10.6 sNorthward80 T
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Tseng, I.-F.; Hsu, C.-H.; Yeh, P.-H.; Lin, T.-C. Physical Mechanism for Seabed Scouring around a Breakwater—A Case Study in Mailiao Port. J. Mar. Sci. Eng. 2022, 10, 1386. https://doi.org/10.3390/jmse10101386

AMA Style

Tseng I-F, Hsu C-H, Yeh P-H, Lin T-C. Physical Mechanism for Seabed Scouring around a Breakwater—A Case Study in Mailiao Port. Journal of Marine Science and Engineering. 2022; 10(10):1386. https://doi.org/10.3390/jmse10101386

Chicago/Turabian Style

Tseng, I-Fan, Chih-Hung Hsu, Po-Hung Yeh, and Ting-Chieh Lin. 2022. "Physical Mechanism for Seabed Scouring around a Breakwater—A Case Study in Mailiao Port" Journal of Marine Science and Engineering 10, no. 10: 1386. https://doi.org/10.3390/jmse10101386

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