A standing wave oscillation in a closed basin,known as a seiche,could cause destruction when its period matches the period of another wave generated by external forces such as wind,quakes,or abrupt changes in atmosphe...A standing wave oscillation in a closed basin,known as a seiche,could cause destruction when its period matches the period of another wave generated by external forces such as wind,quakes,or abrupt changes in atmospheric pressure.It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy,resulting in damages around the area.One condition that might restrict the resonance from occurring is when the bottom friction is present.Therefore,a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena.The study will be conducted for several closed basin shapes.The model will be solved analytically and numerically in order to determine the natural resonant period of the basin,which is the period that can generate a resonance.The computational scheme proposed to solve the model is developed using the staggered grid finite volume method.The numerical scheme will be validated by comparing its results with the analytical solutions.As a result of the comparison,a rather excellent compatibility between the two results is achieved.Furthermore,the impacts that the friction coefficient has on the resonance phenomena are evaluated.It is observed that in the prevention of resonances,the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin.In addition,non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.展开更多
Since the mild-slope equation was derived by Berkhoff （1972）,the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,s...Since the mild-slope equation was derived by Berkhoff （1972）,the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,some scholars applied the mild-slope equation in simulating the tidal motion,which proves that the equation is capable to calculate the tide in actual terrain.But in their studies,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.展开更多
This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly n...This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.展开更多
This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wa...This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term,the surface current and the bottom friction coefficient are defined as the analytical variables,and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient.This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves.Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information.The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments.The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.展开更多
The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom frictio...The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom friction. In this paper,an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thickness, the role of the bottom friction is greater than that of the lateral friction. The model was applied to the Indonesian throughflow and yielded a reduction of approximately 20% in the transport.展开更多
Longwave breaking is the agent for many important upper ocean layer processes including the trans-fer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bot-tom friction was c...Longwave breaking is the agent for many important upper ocean layer processes including the trans-fer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bot-tom friction was considered.In this paper, we discuss the longwave breaking phenomena in the moregeneral case of nth power bottom friction. Using the theory of blowup of solution,the criterion for thetime and location of the longwave breaking can be obtained.展开更多
Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characterist...Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characteristics of the waves propagating on the coral reef flat, the bottom friction coefficients and the transfer of wave energy are discussed in the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the coral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation on the reef flat, the waves sustain more loss in high frequency than in low frequency and the spectral energy transfers to the low frequency. These results may be used for reference in island and reef engineering.展开更多
The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994)...The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.展开更多
文摘A standing wave oscillation in a closed basin,known as a seiche,could cause destruction when its period matches the period of another wave generated by external forces such as wind,quakes,or abrupt changes in atmospheric pressure.It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy,resulting in damages around the area.One condition that might restrict the resonance from occurring is when the bottom friction is present.Therefore,a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena.The study will be conducted for several closed basin shapes.The model will be solved analytically and numerically in order to determine the natural resonant period of the basin,which is the period that can generate a resonance.The computational scheme proposed to solve the model is developed using the staggered grid finite volume method.The numerical scheme will be validated by comparing its results with the analytical solutions.As a result of the comparison,a rather excellent compatibility between the two results is achieved.Furthermore,the impacts that the friction coefficient has on the resonance phenomena are evaluated.It is observed that in the prevention of resonances,the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin.In addition,non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.
基金The Ministry of Education Fundation for the Doctoral Program of Higher Education under contract No.200802940014the Natural Science Foundation of Hohai University under contract Nos 2008430511Ministry of Transport Open Fundation of Laboratry of port,waterway,sediment engineering
文摘Since the mild-slope equation was derived by Berkhoff （1972）,the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,some scholars applied the mild-slope equation in simulating the tidal motion,which proves that the equation is capable to calculate the tide in actual terrain.But in their studies,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.
基金National Natural Science Foundation of China(Grant No.19732004)
文摘This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.
基金supported by the National Natural Science Foundation of China (Nos. 41506039, 41776004, 41775100 and 41606039)the National Key Research and Development Program of China (No. 2016YFC1401800)+1 种基金the Fundamental Research Funds for the Central Universities (No. 2016B12514)the National Programme on Global Change and Air-Sea Interaction of China (No. GASI-IPO VAI-04)
文摘This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term,the surface current and the bottom friction coefficient are defined as the analytical variables,and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient.This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves.Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information.The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments.The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.
基金The National Key Research and Development Program of China under contract No.2016YFC0301103the Scientific and Technological Innovation Project financially supported by Qingdao National Laboratory for Marine Science and Technology under contract No.2015ASKJ01+2 种基金the SOA Program on Global Change and Air-Sea Interactions under contract Nos GASI-IPOVAI-03,GASI-IPOVAI-02 and GASI-IPOVAI-01-02the National Natural Science Foundation of China under contract Nos 40476025,41876027and 41506036the Office of Naval Research of United States under contract No.N00014-08-01-0618
文摘The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom friction. In this paper,an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thickness, the role of the bottom friction is greater than that of the lateral friction. The model was applied to the Indonesian throughflow and yielded a reduction of approximately 20% in the transport.
文摘Longwave breaking is the agent for many important upper ocean layer processes including the trans-fer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bot-tom friction was considered.In this paper, we discuss the longwave breaking phenomena in the moregeneral case of nth power bottom friction. Using the theory of blowup of solution,the criterion for thetime and location of the longwave breaking can be obtained.
文摘Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characteristics of the waves propagating on the coral reef flat, the bottom friction coefficients and the transfer of wave energy are discussed in the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the coral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation on the reef flat, the waves sustain more loss in high frequency than in low frequency and the spectral energy transfers to the low frequency. These results may be used for reference in island and reef engineering.
文摘The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.
