Using plants is a kind of environmentally-friendly coastal protection to attenuate wave energy. In this paper, a set of experiments were conducted to investigate the wave attenuation performance using flexible grasses...Using plants is a kind of environmentally-friendly coastal protection to attenuate wave energy. In this paper, a set of experiments were conducted to investigate the wave attenuation performance using flexible grasses on a submerged slope, and the wave attenuation coefficient for these experiments was calculated for different still water depths, slope and grass configurations. It was found that the slope plays a significant role in wave attenuation. The wave attenuation coefficient increases with increasing relative row number and relative density. For a small relative row number, the two configurations from the slope top to its toe and from the slope toe to its top performed equally to a large extent. For a medium relative row number, the configuration from the slope toe to its top performed more poorly than that from the slope top to its toe; however, it performed better than that from the slope top to its toe for a high relative row number. With a single row of grasses close to the slope top from the slope toe, the wave attenuation coefficient shows double peaks. With increasing grass rows or still water depth, the grass location corresponding to the maximum wave attenuation coefficient is close to the slope top. The dimensional analysis and the least square method were used to derive an empirical equation of the wave attenuation coefficient considering the effect of relative density, the slope, the relative row number and the relative location of the middle row, and the equation was validated to experimental data.展开更多
The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The...The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.’s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns.展开更多
In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, w...In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.展开更多
基金funded by the National Natural Science Foundation of China (No.51579229)State Key Laboratory of Ocean Engineering of China (No.1602)+1 种基金The Key Research and Development Plan of Shandong Province,China (No.2017GHY15103)the Shandong Province Science and Technology Development Plan (No.2014 GHY115026)
文摘Using plants is a kind of environmentally-friendly coastal protection to attenuate wave energy. In this paper, a set of experiments were conducted to investigate the wave attenuation performance using flexible grasses on a submerged slope, and the wave attenuation coefficient for these experiments was calculated for different still water depths, slope and grass configurations. It was found that the slope plays a significant role in wave attenuation. The wave attenuation coefficient increases with increasing relative row number and relative density. For a small relative row number, the two configurations from the slope top to its toe and from the slope toe to its top performed equally to a large extent. For a medium relative row number, the configuration from the slope toe to its top performed more poorly than that from the slope top to its toe; however, it performed better than that from the slope top to its toe for a high relative row number. With a single row of grasses close to the slope top from the slope toe, the wave attenuation coefficient shows double peaks. With increasing grass rows or still water depth, the grass location corresponding to the maximum wave attenuation coefficient is close to the slope top. The dimensional analysis and the least square method were used to derive an empirical equation of the wave attenuation coefficient considering the effect of relative density, the slope, the relative row number and the relative location of the middle row, and the equation was validated to experimental data.
基金financially supported by the Ministry of Science and Technology of Taiwan,China(Grant No.MOST 107-2221-E-992)
文摘The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.’s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns.
基金supported by The Science Council of Taiwan under Grant No. 95-2221-E-005-154
文摘In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.
