2010 Vol.(4)
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2010, (4): 585-596.
Abstract:
The mild-slope equation is familiar to coastal engineers and scientists as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear coordinates show good agreement with the data obtained in three typical physical experiments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.
The mild-slope equation is familiar to coastal engineers and scientists as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear coordinates show good agreement with the data obtained in three typical physical experiments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.
2010, (4): 597-610.
Abstract:
For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are employed as the governing equations. In the model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi matrix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the development of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivates and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the modeled results are in good agreement with the analytical results and experimental data.
For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are employed as the governing equations. In the model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi matrix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the development of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivates and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the modeled results are in good agreement with the analytical results and experimental data.
2010, (4): 611-626.
Abstract:
The effects of various types of waves on vertical plane turbulent jets are studied numerically in the paper. A three-dimensional numerical model in σ -coordinate is developed to study these problems by use of large eddy simulation method. Turbulence is modeled by a dynamic coherent eddy model. Numerical results including the distribution of velocity, the decay law of the mean velocity along axis, the turbulent Reynolds stresses and the volume flux per unit width without wave, in the first-order Stokes waves, in the second-order Stokes waves, in the fifth-order Stokes waves, in the solitary waves and in random waves are compared and analyzed. A focus on coherent structures, probability density functions and correlation functions of jets is also investigated. The numerical results are of great theoretical importance for understanding jet turbulent behaviors in different types of waves.
The effects of various types of waves on vertical plane turbulent jets are studied numerically in the paper. A three-dimensional numerical model in σ -coordinate is developed to study these problems by use of large eddy simulation method. Turbulence is modeled by a dynamic coherent eddy model. Numerical results including the distribution of velocity, the decay law of the mean velocity along axis, the turbulent Reynolds stresses and the volume flux per unit width without wave, in the first-order Stokes waves, in the second-order Stokes waves, in the fifth-order Stokes waves, in the solitary waves and in random waves are compared and analyzed. A focus on coherent structures, probability density functions and correlation functions of jets is also investigated. The numerical results are of great theoretical importance for understanding jet turbulent behaviors in different types of waves.
2010, (4): 627-640.
Abstract:
The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is presented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that both the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater, water particle velocities around the breakwater, and the wave induced pressures on the structure are numerically investigated. The pressure amplitudes of the fundamental and second harmonics on the model surface are examined in various water depths. The computed and experimental results have revealed that the higher frequency components are generated at the onshore side of the breakwater. Furthermore, the computed results demonstrate a circulating flow formed at the onshore side of the breakwater.
The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is presented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that both the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater, water particle velocities around the breakwater, and the wave induced pressures on the structure are numerically investigated. The pressure amplitudes of the fundamental and second harmonics on the model surface are examined in various water depths. The computed and experimental results have revealed that the higher frequency components are generated at the onshore side of the breakwater. Furthermore, the computed results demonstrate a circulating flow formed at the onshore side of the breakwater.
2010, (4): 641-651.
Abstract:
A numerical wave flume is constructed based on the Reynolds Averaged Navier-Stokes (RANS) equations with turbulence closure by a modified k-ε model to study the viscous interactions of waves with vertical breakwaters for different overtopping cases. The governing equations, the turbulence model, boundary conditions, and solution method for the numerical wave flume are introduced briefly. The reliability of the numerical wave flume is examined by comparing the numerical results with the experimental measurements, and good agreements between them indicate the validity of the present model. The developments of mean velocity fields, the contours of vorticity, and the influences of wave nonlinearity on turbulence field as wave passing through vertical breakwaters are discussed in details based on the numerical results. It is noted that the vortices at the rear of the lower submerged breakwater are close to the bottom and maybe induce the scouring to the leeside toe of marine structure in practice. Over all, a conclusion can be obtained from this study that the turbulence in wave field around structure is induced directly by the development of boundary layer on the solid boundary, the nonlinear interaction of free surface with obstacle, and the plunging of overtopping waves.
A numerical wave flume is constructed based on the Reynolds Averaged Navier-Stokes (RANS) equations with turbulence closure by a modified k-ε model to study the viscous interactions of waves with vertical breakwaters for different overtopping cases. The governing equations, the turbulence model, boundary conditions, and solution method for the numerical wave flume are introduced briefly. The reliability of the numerical wave flume is examined by comparing the numerical results with the experimental measurements, and good agreements between them indicate the validity of the present model. The developments of mean velocity fields, the contours of vorticity, and the influences of wave nonlinearity on turbulence field as wave passing through vertical breakwaters are discussed in details based on the numerical results. It is noted that the vortices at the rear of the lower submerged breakwater are close to the bottom and maybe induce the scouring to the leeside toe of marine structure in practice. Over all, a conclusion can be obtained from this study that the turbulence in wave field around structure is induced directly by the development of boundary layer on the solid boundary, the nonlinear interaction of free surface with obstacle, and the plunging of overtopping waves.
2010, (4): 653-662.
Abstract:
The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI=Hmax/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurence in deep water is larger than that in shallow water.
The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI=Hmax/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurence in deep water is larger than that in shallow water.
2010, (4): 663-676.
Abstract:
This paper discusses mumerical results from three-dimensional large eddy simulation of an oscillating cylinder under prescribed movements in uniform flow. Six cases, namely pure in-line, pure cross-flow and two groups of 'Figure of Eight' oscillation patterns are under investigation at Reynolds number Re=24000. The 'Figure of Eight' pattern in each group is with identical shape but opposite orbital directions. The numerical results on hydrodynamic forces, higher order force components, and vortex shedding modes are extensively studied and compared with the measured experimantal data. It is found that the fluid force in phase with the velocity, which represents the energy transfer between the fluid and the cylinder, has opposite sign and different magnitude due to the opposite orbital direction. Higher order force components in cross-flow direction are found to occur at odd number times of the oscillating frequency, while even numbers dominate the opposite orbital direction effect. Comparisons between numerical and experimental results indicate that the present numerical model could be a rational tool for the identification of hydrodynamic coefficients which are normally applied in empirical models to predict the vortex-induced vibrations of slender marine structures.
This paper discusses mumerical results from three-dimensional large eddy simulation of an oscillating cylinder under prescribed movements in uniform flow. Six cases, namely pure in-line, pure cross-flow and two groups of 'Figure of Eight' oscillation patterns are under investigation at Reynolds number Re=24000. The 'Figure of Eight' pattern in each group is with identical shape but opposite orbital directions. The numerical results on hydrodynamic forces, higher order force components, and vortex shedding modes are extensively studied and compared with the measured experimantal data. It is found that the fluid force in phase with the velocity, which represents the energy transfer between the fluid and the cylinder, has opposite sign and different magnitude due to the opposite orbital direction. Higher order force components in cross-flow direction are found to occur at odd number times of the oscillating frequency, while even numbers dominate the opposite orbital direction effect. Comparisons between numerical and experimental results indicate that the present numerical model could be a rational tool for the identification of hydrodynamic coefficients which are normally applied in empirical models to predict the vortex-induced vibrations of slender marine structures.
2010, (4): 677-692.
Abstract:
Vertical structures of momentum exchange coefficient and sediment concentration are the keys in the research on estuarine and coastal suspended sediment transport . Based on the parabolic mixing length distribution pattern, the distribution pattern of vertical momentum exchange coefficient which is suitable for estuarine and coastal waters is constructed. A comparison with steady flow and measured momentum exchange coefficient during one tidal cycle in Menai Strait of England shows that the result of this pattern is closer to the measured values than those of commonly used Rouse's and van Rijn's patterns, and the pattern is also suitable for estuarine and coastal waters. Successively, based on the precondition that momentum exchange coefficient is equivalent to sediment turbulent diffusion coefficient, and combining with the Diffusion Theory, we obtain the exponential vertical distribution pattern of sediment concentration, which is also suitable for estuarine and coastal waters. Thereby, using measured vertical stratified sediment concentration data of south and north passage of Yangtze Estuary and Zhoushan archipelago waters for fitting calculation, and comparing the results with those from Rouse's (1938) and Zhang et al.'s (1989) formulas, the results show that the exponential vertical distribution pattern of sediment concentration obtained in the present paper not only overcomes the defect of Rouse's Formula that the surface sediment concentration will be 0, but also has a holistic higher precision along the vertical lines than those of Rouse’s and Zhang et al.’s formulas.
Vertical structures of momentum exchange coefficient and sediment concentration are the keys in the research on estuarine and coastal suspended sediment transport . Based on the parabolic mixing length distribution pattern, the distribution pattern of vertical momentum exchange coefficient which is suitable for estuarine and coastal waters is constructed. A comparison with steady flow and measured momentum exchange coefficient during one tidal cycle in Menai Strait of England shows that the result of this pattern is closer to the measured values than those of commonly used Rouse's and van Rijn's patterns, and the pattern is also suitable for estuarine and coastal waters. Successively, based on the precondition that momentum exchange coefficient is equivalent to sediment turbulent diffusion coefficient, and combining with the Diffusion Theory, we obtain the exponential vertical distribution pattern of sediment concentration, which is also suitable for estuarine and coastal waters. Thereby, using measured vertical stratified sediment concentration data of south and north passage of Yangtze Estuary and Zhoushan archipelago waters for fitting calculation, and comparing the results with those from Rouse's (1938) and Zhang et al.'s (1989) formulas, the results show that the exponential vertical distribution pattern of sediment concentration obtained in the present paper not only overcomes the defect of Rouse's Formula that the surface sediment concentration will be 0, but also has a holistic higher precision along the vertical lines than those of Rouse’s and Zhang et al.’s formulas.
2010, (4): 693-708.
Abstract:
Based on the model test of podded propulsor in straight forward motion, the paper presents the results of the effects of geometric parameters on the propulsive characteristics of podded propulsors in viscous flow. Three main geometrical parameters, i.e. pod diameter, strut distance from the propeller plane, and the maximum thickness of strut were studied with systematically varied geometry while the parameters of propeller blades are fixed. The RANS approach is adopted to study the steady performance using the Fluent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed to predict the steady performance. In consideration of the complexity, the research does not deal with the effects of the combination of such three main parameters.
Based on the model test of podded propulsor in straight forward motion, the paper presents the results of the effects of geometric parameters on the propulsive characteristics of podded propulsors in viscous flow. Three main geometrical parameters, i.e. pod diameter, strut distance from the propeller plane, and the maximum thickness of strut were studied with systematically varied geometry while the parameters of propeller blades are fixed. The RANS approach is adopted to study the steady performance using the Fluent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed to predict the steady performance. In consideration of the complexity, the research does not deal with the effects of the combination of such three main parameters.
2010, (4): 709-724.
Abstract:
To understand the mooring energy during positioning, the expressions of four items concerning mooring line energy are presented based on a finite element model, including gravitational and elastic potential energy, kinetic energy and dissipated energy due to mooring-induced damping. In a static case, the force calculated from the derivative of potential energy with respect to distance is compared with that of direct calculation. The results are found fit well, which indicates the law of conservation of energy and also shows the correctness of the potential energy results. For the cases of a single mooring line with the attachment point oscillating with different amplitudes in horizontal or vertical direction (corresponding to surge and roll motions respectively), and the case of the mooring line with a horizontal bichromatic oscillation on the attachment point, the time history of the first three items are calculated and analyzed, also, the indicator diagram for mooring-induced damping are given. These results reveal the energy state of the mooring line and can provide a better understanding of how mooring line works.
To understand the mooring energy during positioning, the expressions of four items concerning mooring line energy are presented based on a finite element model, including gravitational and elastic potential energy, kinetic energy and dissipated energy due to mooring-induced damping. In a static case, the force calculated from the derivative of potential energy with respect to distance is compared with that of direct calculation. The results are found fit well, which indicates the law of conservation of energy and also shows the correctness of the potential energy results. For the cases of a single mooring line with the attachment point oscillating with different amplitudes in horizontal or vertical direction (corresponding to surge and roll motions respectively), and the case of the mooring line with a horizontal bichromatic oscillation on the attachment point, the time history of the first three items are calculated and analyzed, also, the indicator diagram for mooring-induced damping are given. These results reveal the energy state of the mooring line and can provide a better understanding of how mooring line works.
2010, (4): 725-733.
Abstract:
Based on the analysis of tropical cyclone (TC) database in the Northwest Pacific (NWP) from 1945 to 2008, we not only extract the temporal variation of TC intensity and frequency, but also give their spatial distribution both in the NWP and in the South China Sea (SCS). The results show that there is an observational increase of TC activities, which manifests as the enhancement of the power dissipation index (PDI) and the growth of TC frequency, especially for typhoons and strong typhoons. The inhomogeneous spatial distributions of TC frequency and intensity are also provided both in the NWP and in the SCS. For example, the region of Zhongsha Islands and Dongsha Islands in the SCS (15o~22oN, 115o~120oE), west to the Philippine Islands is the place with frequent occurrence of strong typhoons, among which the wind speed of 7 TCs in 64 years exceeds 60 m/s.
Based on the analysis of tropical cyclone (TC) database in the Northwest Pacific (NWP) from 1945 to 2008, we not only extract the temporal variation of TC intensity and frequency, but also give their spatial distribution both in the NWP and in the South China Sea (SCS). The results show that there is an observational increase of TC activities, which manifests as the enhancement of the power dissipation index (PDI) and the growth of TC frequency, especially for typhoons and strong typhoons. The inhomogeneous spatial distributions of TC frequency and intensity are also provided both in the NWP and in the SCS. For example, the region of Zhongsha Islands and Dongsha Islands in the SCS (15o~22oN, 115o~120oE), west to the Philippine Islands is the place with frequent occurrence of strong typhoons, among which the wind speed of 7 TCs in 64 years exceeds 60 m/s.
2010, (4): 735-748.
Abstract:
Surface elevation is the basic data for geo-science. It is difficult to retrieve tidal-flats’ elevation from single Remote Sensing (RS) image because of the complicated sediment dynamical environment and huge spatial difference in tidal-flats’ moisture content. A Digital Elevation Model (DEM) construction method for inconstant inter-tidal zone based on high tempo-resolution MODIS data set in a short period is proposed in a case study on the Dongsha Sandbank of the Jiangsu Radial Tidal Sand-ridges. In the present study, a batch-preprocessing method based on image partition to handle massive MODIS 1B images is developed and applied to 8163 scenes of MODIS images. The dataset of short-period and multi-temporal MODIS images for inter-tidal flats’ DEM inversion is selected and the usability of MODIS dataset is analyzed. Shorelines of the Dongsha Sandbank are extracted by use of batch supervised classification. In accord with tidal-level forecasted by the Chenjiawu Tidal Gauge Station at the overpass moment of each RS image, DEMs of inter-tidal flats in January and summer(Jul, Aug and Sept), 2003 were built under ArcGIS9.2. Studies show that: (1) The dataset of short-duration and multi-phase MODIS images can be used to retrieve the historical DEM of tidal-flats at changeful tidal flats. (2) Analysis on usability of MODIS images from Aqua and Terra indicates that there are more usable and high-quality MODIS images in spring, autumn and winter, but less in summer. Therefore, the period for building inter-tidal flats’ DEM is suggested to be one month in spring, autumn and winter and three months in summer.
Surface elevation is the basic data for geo-science. It is difficult to retrieve tidal-flats’ elevation from single Remote Sensing (RS) image because of the complicated sediment dynamical environment and huge spatial difference in tidal-flats’ moisture content. A Digital Elevation Model (DEM) construction method for inconstant inter-tidal zone based on high tempo-resolution MODIS data set in a short period is proposed in a case study on the Dongsha Sandbank of the Jiangsu Radial Tidal Sand-ridges. In the present study, a batch-preprocessing method based on image partition to handle massive MODIS 1B images is developed and applied to 8163 scenes of MODIS images. The dataset of short-period and multi-temporal MODIS images for inter-tidal flats’ DEM inversion is selected and the usability of MODIS dataset is analyzed. Shorelines of the Dongsha Sandbank are extracted by use of batch supervised classification. In accord with tidal-level forecasted by the Chenjiawu Tidal Gauge Station at the overpass moment of each RS image, DEMs of inter-tidal flats in January and summer(Jul, Aug and Sept), 2003 were built under ArcGIS9.2. Studies show that: (1) The dataset of short-duration and multi-phase MODIS images can be used to retrieve the historical DEM of tidal-flats at changeful tidal flats. (2) Analysis on usability of MODIS images from Aqua and Terra indicates that there are more usable and high-quality MODIS images in spring, autumn and winter, but less in summer. Therefore, the period for building inter-tidal flats’ DEM is suggested to be one month in spring, autumn and winter and three months in summer.
2010, (4): 749-758.
Abstract:
The fluctuating forces of the fluid exerted on the top tensioned riser (TTR) in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations (VIV) of the riser are analyzed in time domain in this paper. The numerical simulation results of the riser’s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser’s VIV. Finally, the effects of the riser’s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.
The fluctuating forces of the fluid exerted on the top tensioned riser (TTR) in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations (VIV) of the riser are analyzed in time domain in this paper. The numerical simulation results of the riser’s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser’s VIV. Finally, the effects of the riser’s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.
2010, (4): 759-770.
Abstract:
Ship waves are observed with wave-generating techniques by way of simulating express liners in the Zhujiang Delta. The analog test study of ship waves is conducted in a wave flume and a wave basin respectively. Thus, different wave elements and different incident angles of ship waves are decided; so are different slopes of protection, the platform, width of platform, and the influence over the ship wave run-up on protection from armor coat structure. The empirical relationship, adaptable to ship wave run-up slopes protection, is obtained. The reference foundations are provided for the design of the protection under the ship wave action of express liners in the inland waterway of the Zhujiang Delta.
Ship waves are observed with wave-generating techniques by way of simulating express liners in the Zhujiang Delta. The analog test study of ship waves is conducted in a wave flume and a wave basin respectively. Thus, different wave elements and different incident angles of ship waves are decided; so are different slopes of protection, the platform, width of platform, and the influence over the ship wave run-up on protection from armor coat structure. The empirical relationship, adaptable to ship wave run-up slopes protection, is obtained. The reference foundations are provided for the design of the protection under the ship wave action of express liners in the inland waterway of the Zhujiang Delta.
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