After a check that the solver is appropriate to solve a comparable 2-D application on solid–fluid interaction, it was used to study a real situation on the Chinese coast. A mariculture platform on the coast of Xiapu in China was studied here (Figure 10
). The mariculture platform rears marine fish, large yellow croaker mostly, in cages suspended by floating rafts in coastal areas. The dimension of the cages ranges from a few meters to tens of meters, and the fishermen can walk and work on the floating frame. In this study, the 3-DoF motion of a large-scale mariculture platform with dimension of 20 m was simulated with realistic wave conditions by DualSPHysics.
The safety of fishermen and fish products should be highly valued in the mariculture platform. Regarding the safety of fishermen, according to the “Shallow Sea Mobile Platform Towing and Mooring Safety Regulations” [42
] issued by the Chinese National Energy Administration, operations offshore need to be carried out when the wave height is less than 1 m. With reference to the safety guidelines for offshore floating platforms defined by Xie Guangci [43
], the surge of the platform should not exceed 20% of the water depth, heave should not exceed 10% of the water depth, and the pitch angle under operating conditions should be less than 5°. Regarding the safety of fish products, we only consider the fish escape risks that may occur when the platform is submerged, tilted, and reversed in this work.
The following were the conditions of the initial setup of the numerical tank: (i) the simulation was 2-D for a section of the mariculture platform; (ii) proper wave generation and propagation was guaranteed because the tank was long enough; (iii) the dimensions used for the mariculture platform were the real ones; (iv) the regular waves were generated by a piston wavemaker using the measured wave heights and periods in that area. Figure 11
shows the numerical tank setup: the tank was 190 m in length, the piston wavemaker sat on the left side, the beach sat on the right side, the water depth was set as a realistic depth of this area, and the still-water depth was 10 m at the piston location.
The goal of this simulation was to mimic the 3-DoF motions of a simplified mariculture platform with two realistic wave conditions: a typical wave and a typhoon wave.
4.1. 3-DoF under a Typical Annual Wave
The typical annual wave was analyzed using the in situ buoy data, which show the real sea state of this area. The buoy is 18 km away from the mariculture platform and has been used to collect one year of wave data. The typical annual wave, which is the observed one-year significant wave height with a cumulative frequency of 75%, has a height of 0.6 m and period of 5 s. The regular and irregular waves were numerically reproduced. The waves had intermediate depths according to the values of the relative depth (d/L
). Then, Stokes second-order wave theory was used to determine the wave kinematics of the test (Figure 5
First, we validated the wave propagation obtained by comparing the numerical and theoretical values. The theoretical values were calculated using Stokes second-order wave theory. Figure 12
compares the theoretical and simulated surface elevations for a regular wave at WG1, WG2, and WG3 which is 10, 20, and 30 m from the wavemaker. The simulated SPH surface elevations follow Stokes second-order wave theory, demonstrating that waves are generated and propagated properly.
The waves generated and propagated by DualSPHysics have been proven accurate. The behavior of an open sea can be reproduced by a piston wavemaker in DualSPHysics, and the real sea state can also be mimicked. DualSPHysics can also be used to study the interaction between the waves and the mariculture platform on the coast of Xiapu. Therefore, DualSPHysics can be used to compute the 3-DoF motions of the mariculture platform. Figure 13
shows the simulated surge, heave, and pitch of the mariculture platform under the regular and irregular waves with H = 0.6 m and T = 5 s.
The experimental results for the regular wave reveal that the surge, heave, and pitch were steadily periodic after 15 wave periods. The surge results under the regular wave show that, within a wave period, the mariculture platform drifted back and forth in the wave propagation direction with a displacement of 0.22 m. The platform was not taken away by the wave with the restriction from moorings. The heave and pitch results for the regular wave show that, within a wave period, the mariculture platform was lifted up and down with an amplitude of 0.11 m and pitched periodically with a range of 3.4°.
The experimental results for the irregular wave show that the mariculture platform can be carried up to 0.42 m away from the original position, lifted up and down with an amplitude of 0.14 m, and pitched periodically with a range of 3.9°.
In this typical annual sea wave condition, the mariculture platform will not be rushed away or overturned. The fishermen are relatively safe if they stay and work on it, and the impact on fish activities in the cage is small. The design of the mariculture platform is appropriate.
4.2. 3-DoF under Typhoon Dujuan Waves
The coast of Xiapu in China endures high-frequency typhoon disasters. Typhoon Dujuan in 2015 landed 200 km away from this mariculture platform and caused extreme waves here. The maximum significant wave height recorded by the buoy, which is 18 km away from the mariculture platform, was 3.7 m with a period of 9.9 s. When the maximum significant wave height was present, the water level observed at the tidal gauge located 24 km away from the mariculture platform was 1.88 m. As we can see from Figure 14
, the waves had intermediate depths, and the regular and irregular waves followed Stokes second-order wave theory. Therefore, the experiments were conducted under a regular wave and irregular wave with H = 3.7 m, T = 9.9 s, and a still-water depth set as d = 11.88 m. These experiments duplicated the most dangerous situations of the mariculture platform during Typhoon Dujuan.
shows the simulated surge, heave, and pitch of the mariculture platform under the regular and irregular waves with H = 3.7 m, T = 9.9 s, and a water level of 1.88 m.
The experimental results for the regular wave reveal that the heave and pitch have steady periodic motion after four wave periods. The mariculture platform drifted 2.5 m away from the original position even with the restriction from mooring, and drifted back and forth in the wave propagation direction with a displacement of 5.1 m. The mariculture platform was lifted up and down with an amplitude of 1.5 m and pitched periodically with a range of 14°.
The irregular-wave experimental results show that the mariculture platform can be carried up to 8.9 m away from the original position, lifted up and down with an amplitude of 1.6 m, and pitched periodically with a range of 20°.
shows the snapshot of the mariculture platform with the largest pitch angle (9.18°) under the regular wave with H = 3.7 m and T = 9.9 s. The fish escape is likely occurring because of the platform tilts. Further, the escape might result in large property loss.
In this dangerous situation of extreme wave action, the mariculture platform experiences vigorous movement. It is not safe for the fishermen to stay and work, injuries from collision with fish and cages, and fish escapes may also occur.
To evaluate the impact of tidal water level variation on the hydrodynamic behavior of the mariculture platform, we conducted three experiments with different water levels. The experiments were designed on the basis of the wave and tidal level observations of the area adjacent to the mariculture platform. The mean high-tide level, mean tide level, and mean low-tide level were 3.64, 0.78, and −2.07 m, which were the levels observed at the nearest tidal gauge during the two days before Typhoon Dujuan landed. The average significant wave height, which was observed at the nearest buoy during the two days before Typhoon Dujuan landed, was 1.5 m.
Then, the experiments were conducted under regular waves with H = 1.5 m and T = 7.4 s, and the still-water depth was set as d = 13.64 m, 10.78 m, and 7.93 m. The wave had intermediate depths, and the regular wave was determined by Stokes second-order wave theory (Figure 5
). Figure 15
shows the simulated surge, heave, and pitch of the mariculture platform under the regular wave with H = 1.5 m and T = 7.4 s when the water level was 3.64, 0.78, and −2.07 m.
As we can see from Figure 16
, the mariculture platform moved in advance, about half a period, with the increasing water depth under the same wave condition. The surge shrunk and the pitch angle decreased as the water depth grew. Ocean waves propagated in the intermediate-depth water, and the increasing water depth increased the wave propagation speed. This led the wave to be elongated and deformed, and the wave height decreased. As a result, there was an earlier motion response and smaller motion range.
In the average wave action of Typhoon Dujuan, the mariculture platform experiences vigorous movement. It is not safe for fishermen to stay and work, and injuries from collision with fish and cages may also occur. The analysis above reminds us that the fishermen should be evacuated, and the fish should be harvested or transferred before the typhoon arrives.