2017 Vol.31(6)
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2017, 31(6): 653-664.
doi: 10.1007/s13344-017-0075-5
Abstract:
Severe slugging can occur in a pipeline-riser system at relatively low liquid and gas flow rates during gas-oil transportation, possibly causing unexpected damage to the production facilities. Experiments with air and water are conducted in a horizontal and downward inclined pipeline followed by a catenary riser in order to investigate the mechanism and characteristics of severe slugging. A theoretical model is introduced to compare with the experiments. The results show that the formation mechanism of severe slugging in a catenary riser is different from that in a vertical riser due to the riser geometry and five flow patterns are obtained and analyzed. A gas-liquid mixture slug stage is observed at the beginning of one cycle of severe slugging, which is seldom noticed in previous studies. Based on both experiments and computations, the time period and variation of pressure amplitude of severe slugging are found closely related to the superficial gas velocity, implying that the gas velocity significantly influences the flow patterns in our experiments. Moreover, good agreements between the experimental data and the numerical results are shown in the stability curve and flow regime map, which can be a possible reference for design in an offshore oil-production system.
Severe slugging can occur in a pipeline-riser system at relatively low liquid and gas flow rates during gas-oil transportation, possibly causing unexpected damage to the production facilities. Experiments with air and water are conducted in a horizontal and downward inclined pipeline followed by a catenary riser in order to investigate the mechanism and characteristics of severe slugging. A theoretical model is introduced to compare with the experiments. The results show that the formation mechanism of severe slugging in a catenary riser is different from that in a vertical riser due to the riser geometry and five flow patterns are obtained and analyzed. A gas-liquid mixture slug stage is observed at the beginning of one cycle of severe slugging, which is seldom noticed in previous studies. Based on both experiments and computations, the time period and variation of pressure amplitude of severe slugging are found closely related to the superficial gas velocity, implying that the gas velocity significantly influences the flow patterns in our experiments. Moreover, good agreements between the experimental data and the numerical results are shown in the stability curve and flow regime map, which can be a possible reference for design in an offshore oil-production system.
2017, 31(6): 665-673.
doi: 10.1007/s13344-017-0076-4
Abstract:
This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.
This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.
2017, 31(6): 674-682.
doi: 10.1007/s13344-017-0077-3
Abstract:
This paper proposes a structure combined by baffle and submerged breakwater (abbreviated to SCBSB in the following texts). Such a combined structure is conducive to the water exchange in the harbor, and has strong capability on wave dissipation. Our paper focuses on the discussion of two typical structures, i.e., the submerged baffle and rectangular breakwater combined with the upper baffle respectively, which are named as SCBSB1 and SCBSB2 for short. The eigenfunction method corrected by experimental results is used to investigate the wave dissipation characteristics. It shows that the calculated results agree well with the experimental data and the minimum value of the wave transmission coefficient can be obtained when the distance between the front and rear structures is from 1/4 to 1/2 of the incident wave length.
This paper proposes a structure combined by baffle and submerged breakwater (abbreviated to SCBSB in the following texts). Such a combined structure is conducive to the water exchange in the harbor, and has strong capability on wave dissipation. Our paper focuses on the discussion of two typical structures, i.e., the submerged baffle and rectangular breakwater combined with the upper baffle respectively, which are named as SCBSB1 and SCBSB2 for short. The eigenfunction method corrected by experimental results is used to investigate the wave dissipation characteristics. It shows that the calculated results agree well with the experimental data and the minimum value of the wave transmission coefficient can be obtained when the distance between the front and rear structures is from 1/4 to 1/2 of the incident wave length.
2017, 31(6): 683-692.
doi: 10.1007/s13344-017-0078-2
Abstract:
Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.
Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.
2017, 31(6): 693-699.
doi: 10.1007/s13344-017-0079-1
Abstract:
A new technology of offshore oil rod pumping production is developed for offshore heavy oil recovery. A new type of miniature hydraulic pumping unit with long-stroke, low pumping speed and compact structure is designed based on the spatial characteristics of offshore platforms. By combining the strengths of sinusoidal velocity curve and trapezoidal velocity curve, a kinematical model of the acceleration, the velocity and displacement of the pumping unit’s hanging point is established. The results show that the pumping unit has good kinematic characteristics of smooth motion and small dynamic load. The multi-degree-of-freedom dynamic model of the single-well pumping unit is established. The first and second order natural frequencies of the sucker rod string subsystem and the pumping unit subsystem are studied. The results show that the first and the second order natural frequencies among the pumping rod string, pumping unit-platform subsystem and the dynamic excitation have differences over 5 times from each other, indicating that resonance phenomenon will not appear during the operation and the dynamic requirements for field use are met in the system.
A new technology of offshore oil rod pumping production is developed for offshore heavy oil recovery. A new type of miniature hydraulic pumping unit with long-stroke, low pumping speed and compact structure is designed based on the spatial characteristics of offshore platforms. By combining the strengths of sinusoidal velocity curve and trapezoidal velocity curve, a kinematical model of the acceleration, the velocity and displacement of the pumping unit’s hanging point is established. The results show that the pumping unit has good kinematic characteristics of smooth motion and small dynamic load. The multi-degree-of-freedom dynamic model of the single-well pumping unit is established. The first and second order natural frequencies of the sucker rod string subsystem and the pumping unit subsystem are studied. The results show that the first and the second order natural frequencies among the pumping rod string, pumping unit-platform subsystem and the dynamic excitation have differences over 5 times from each other, indicating that resonance phenomenon will not appear during the operation and the dynamic requirements for field use are met in the system.
2017, 31(6): 700-708.
doi: 10.1007/s13344-017-0080-8
Abstract:
Fuel consumption in fisheries is a primary concern because of its effects on the environment and the costs incurred by fishermen. Many studies have been conducted to reduce the fuel consumption in fishing operations. Fuel consumption due to fishing gear during a fishing operation is generally related to the hydrodynamic resistance on the gear. This means that fuel consumption is proportional to the drag created by the towing speed. Based on numerical methods, this study suggests a new approach to reduce fuel consumption in fisheries. The results of the simulation are in good agreement with those of model experiments. The total as well as partial resistance forces on the gear are calculated by simulation. The simulation results suggest improved materials and gear structure for reducing the hydrodynamic forces on the gear while maintaining gear performance. The method for assessing the gear performance involves measuring the height and width of the net mouth. Furthermore, this study investigates the efficiency of a low-energy trawl from an economic point of view. The findings of this study will be useful in reducing greenhouse gas (GHG) emissions in fishing operations, and thereby contribute toward lowering fishing costs by saving fuel.
Fuel consumption in fisheries is a primary concern because of its effects on the environment and the costs incurred by fishermen. Many studies have been conducted to reduce the fuel consumption in fishing operations. Fuel consumption due to fishing gear during a fishing operation is generally related to the hydrodynamic resistance on the gear. This means that fuel consumption is proportional to the drag created by the towing speed. Based on numerical methods, this study suggests a new approach to reduce fuel consumption in fisheries. The results of the simulation are in good agreement with those of model experiments. The total as well as partial resistance forces on the gear are calculated by simulation. The simulation results suggest improved materials and gear structure for reducing the hydrodynamic forces on the gear while maintaining gear performance. The method for assessing the gear performance involves measuring the height and width of the net mouth. Furthermore, this study investigates the efficiency of a low-energy trawl from an economic point of view. The findings of this study will be useful in reducing greenhouse gas (GHG) emissions in fishing operations, and thereby contribute toward lowering fishing costs by saving fuel.
2017, 31(6): 709-715.
doi: 10.1007/s13344-017-0081-7
Abstract:
Combining high precision numerical analysis methods with optimization algorithms to make a systematic exploration of a design space has become an important topic in the modern design methods. During the design process of an underwater glider’s flying-wing structure, a surrogate model is introduced to decrease the computation time for a high precision analysis. By these means, the contradiction between precision and efficiency is solved effectively. Based on the parametric geometry modeling, mesh generation and computational fluid dynamics analysis, a surrogate model is constructed by adopting the design of experiment (DOE) theory to solve the multi-objects design optimization problem of the underwater glider. The procedure of a surrogate model construction is presented, and the Gaussian kernel function is specifically discussed. The Particle Swarm Optimization (PSO) algorithm is applied to hydrodynamic design optimization. The hydrodynamic performance of the optimized flying-wing structure underwater glider increases by 9.1%.
Combining high precision numerical analysis methods with optimization algorithms to make a systematic exploration of a design space has become an important topic in the modern design methods. During the design process of an underwater glider’s flying-wing structure, a surrogate model is introduced to decrease the computation time for a high precision analysis. By these means, the contradiction between precision and efficiency is solved effectively. Based on the parametric geometry modeling, mesh generation and computational fluid dynamics analysis, a surrogate model is constructed by adopting the design of experiment (DOE) theory to solve the multi-objects design optimization problem of the underwater glider. The procedure of a surrogate model construction is presented, and the Gaussian kernel function is specifically discussed. The Particle Swarm Optimization (PSO) algorithm is applied to hydrodynamic design optimization. The hydrodynamic performance of the optimized flying-wing structure underwater glider increases by 9.1%.
2017, 31(6): 716-723.
doi: 10.1007/s13344-017-0082-6
Abstract:
In the present research, effect of silica fume as an additive and oil polluted sands as aggregates on compressive strength of concrete were investigated experimentally. The amount of oil in the designed mixtures was assumed to be constant and equal to 2% of the sand weight. Silica fume accounting for 10%, 15% and 20% of the weight is added to the designed mixture. After preparation and curing, concrete specimens were placed into the three different conditions: fresh, brackish and saltwater environments (submerged in fresh water, alternation of exposed in air & submerged in sea water and submerged in sea water). The result of compressive strength tests shows that the compressive strength of the specimens consisting of silica fume increases significantly in comparison with the control specimens in all three environments. The compressive strength of the concrete with 15% silica fume content was about 30% to 50% higher than that of control specimens in all tested environments under the condition of using polluted aggregates in the designed mixture.
In the present research, effect of silica fume as an additive and oil polluted sands as aggregates on compressive strength of concrete were investigated experimentally. The amount of oil in the designed mixtures was assumed to be constant and equal to 2% of the sand weight. Silica fume accounting for 10%, 15% and 20% of the weight is added to the designed mixture. After preparation and curing, concrete specimens were placed into the three different conditions: fresh, brackish and saltwater environments (submerged in fresh water, alternation of exposed in air & submerged in sea water and submerged in sea water). The result of compressive strength tests shows that the compressive strength of the specimens consisting of silica fume increases significantly in comparison with the control specimens in all three environments. The compressive strength of the concrete with 15% silica fume content was about 30% to 50% higher than that of control specimens in all tested environments under the condition of using polluted aggregates in the designed mixture.
2017, 31(6): 724-735.
doi: 10.1007/s13344-017-0083-5
Abstract:
This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons on the basis of the plane wave hypothesis and full wave model. The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=(2n+1)π (n=0, 1, 2, 3, …), rather than kh=nπ (n=0, 1, 2, 3, …); the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L<1 (2b, grating constant; L, wave length) and the lower bound is h/b≤1. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.
This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons on the basis of the plane wave hypothesis and full wave model. The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=(2n+1)π (n=0, 1, 2, 3, …), rather than kh=nπ (n=0, 1, 2, 3, …); the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L<1 (2b, grating constant; L, wave length) and the lower bound is h/b≤1. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.
2017, 31(6): 736-746.
doi: 10.1007/s13344-017-0084-4
Abstract:
In order to accurately simulate strong three-dimensional (3-D) free surface flows and sediment transport, the fully 3-D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection–diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional (2-D) grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.
In order to accurately simulate strong three-dimensional (3-D) free surface flows and sediment transport, the fully 3-D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection–diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional (2-D) grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.
2017, 31(6): 747-753.
doi: 10.1007/s13344-017-0085-3
Abstract:
Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H1/10) causes the similar damage as regular waves.
Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H1/10) causes the similar damage as regular waves.
2017, 31(6): 754-763.
doi: 10.1007/s13344-017-0086-2
Abstract:
The present research aims at clarifying the effects of freak wave on the motion and dynamic responses of a semisubmersible. To reveal the effects of mooring stiffness, two mooring systems were employed in the model tests and time-domain simulations. The 6-DOF motion responses and mooring tensions have been measured and the 3-DOF motions of fairleads were calculated as well. From the time series, trajectories and statistics information, the interactions between the freak wave and the semisubmersible have been demonstrated and the effects of mooring stiffness have been identified. The shortage of numerical simulations based on 3D potential flow theory is presented. Results show that the freak wave is likely to cause large horizontal motions for soft mooring system and to result in extremely large mooring tensions for tight mooring system. Therefore, the freak wave is a real threat for the marine structure, which needs to be carefully considered at design stage.
The present research aims at clarifying the effects of freak wave on the motion and dynamic responses of a semisubmersible. To reveal the effects of mooring stiffness, two mooring systems were employed in the model tests and time-domain simulations. The 6-DOF motion responses and mooring tensions have been measured and the 3-DOF motions of fairleads were calculated as well. From the time series, trajectories and statistics information, the interactions between the freak wave and the semisubmersible have been demonstrated and the effects of mooring stiffness have been identified. The shortage of numerical simulations based on 3D potential flow theory is presented. Results show that the freak wave is likely to cause large horizontal motions for soft mooring system and to result in extremely large mooring tensions for tight mooring system. Therefore, the freak wave is a real threat for the marine structure, which needs to be carefully considered at design stage.
2017, 31(6): 764-772.
doi: 10.1007/s13344-017-0087-1
Abstract:
Till now, there have been lots of researches on numerical simulation of vortex-induced vibration. Acceptable results have been obtained for fixed cylinders with low Reynolds number. However, for responses of 2-DOF vortex-induced vibration with low mass ratio, the accuracy is not satisfactory, especially for the maximum amplitudes. In Jauvtis and Williamson’s work, the maximum amplitude of the cylinder with low mass ratio m*=2.6 can reach as large as 1.5D to be called as the " super-upper branch”, but from current literatures, few simulation results can achieve such value, even fail to capture the upper branch. Besides, it is found that the amplitude decays too fast in the lower branch with the RANS-based turbulence model. The reason is likely to be the defects of the turbulence model itself in the prediction of unsteady separated flows as well as the unreasonable setting of the numerical simulation parameters. Aiming at above issues, a modified turbulence model is proposed in this paper, and the effect of the acceleration of flow field on the response of vortex-induced vibration is studied based on OpenFOAM. By analyzing the responses of amplitude, phase and trajectory, frequency and vortex mode, it is proved that the vortex-induced vibration can be predicted accurately with the modified turbulence model under appropriate flow field acceleration.
Till now, there have been lots of researches on numerical simulation of vortex-induced vibration. Acceptable results have been obtained for fixed cylinders with low Reynolds number. However, for responses of 2-DOF vortex-induced vibration with low mass ratio, the accuracy is not satisfactory, especially for the maximum amplitudes. In Jauvtis and Williamson’s work, the maximum amplitude of the cylinder with low mass ratio m*=2.6 can reach as large as 1.5D to be called as the " super-upper branch”, but from current literatures, few simulation results can achieve such value, even fail to capture the upper branch. Besides, it is found that the amplitude decays too fast in the lower branch with the RANS-based turbulence model. The reason is likely to be the defects of the turbulence model itself in the prediction of unsteady separated flows as well as the unreasonable setting of the numerical simulation parameters. Aiming at above issues, a modified turbulence model is proposed in this paper, and the effect of the acceleration of flow field on the response of vortex-induced vibration is studied based on OpenFOAM. By analyzing the responses of amplitude, phase and trajectory, frequency and vortex mode, it is proved that the vortex-induced vibration can be predicted accurately with the modified turbulence model under appropriate flow field acceleration.
2017, 31(6): 773-780.
doi: 10.1007/s13344-017-0088-0
Abstract:
In this study, a dynamic modeling method for foil-like underwater vehicles is introduced and experimentally verified in different sea tests of the Hadal ARV. The dumping force of a foil-like underwater vehicle is sensitive to swing motion. Some foil-like underwater vehicles swing periodically when performing a free-fall dive task in experiments. Models using conventional modeling methods yield solutions with asymptotic stability, which cannot simulate the self-sustained swing motion. By improving the ridge regression optimization algorithm, a grey-box modeling method based on 378 viscous drag coefficients using the Taylor series expansion is proposed in this study. The method is optimized for over-fitting and convergence problems caused by large parameter matrices. Instead of the PMM test data, the unsteady computational fluid dynamics calculation results are used in modeling. The obtained model can better simulate the swing motion of the underwater vehicle. Simulation and experimental results show a good consistency in free-fall tests during sea trials, as well as a prediction of the dive speed in the swing state.
In this study, a dynamic modeling method for foil-like underwater vehicles is introduced and experimentally verified in different sea tests of the Hadal ARV. The dumping force of a foil-like underwater vehicle is sensitive to swing motion. Some foil-like underwater vehicles swing periodically when performing a free-fall dive task in experiments. Models using conventional modeling methods yield solutions with asymptotic stability, which cannot simulate the self-sustained swing motion. By improving the ridge regression optimization algorithm, a grey-box modeling method based on 378 viscous drag coefficients using the Taylor series expansion is proposed in this study. The method is optimized for over-fitting and convergence problems caused by large parameter matrices. Instead of the PMM test data, the unsteady computational fluid dynamics calculation results are used in modeling. The obtained model can better simulate the swing motion of the underwater vehicle. Simulation and experimental results show a good consistency in free-fall tests during sea trials, as well as a prediction of the dive speed in the swing state.
2017, 31(6): 781-787.
doi: 10.1007/s13344-017-0089-z
Abstract:
Based on the Stokes wave theory, the capillary-gravity wave and the interfacial internal wave in two-layer constant depth’s fluid system are investigated. The fluids are assumed to be incompressible, inviscid and irrotational. The third-order Stokes wave solutions are given by using a perturbation method. The results indicate that the third-order solutions depend on the surface tension, the density and the depth of each layer. As expected, the first-order solutions are the linear theoretical results (the small amplitude wave theoretical results). The second-order and the third-order solutions describe the nonlinear modification and the nonlinear interactions. The nonlinear impact appears not only in the n (n≥2) times’ high frequency components, but also in the low frequency components. It is also noted that the wave velocity depends on the wave number, depth, wave amplitude and surface tension.
Based on the Stokes wave theory, the capillary-gravity wave and the interfacial internal wave in two-layer constant depth’s fluid system are investigated. The fluids are assumed to be incompressible, inviscid and irrotational. The third-order Stokes wave solutions are given by using a perturbation method. The results indicate that the third-order solutions depend on the surface tension, the density and the depth of each layer. As expected, the first-order solutions are the linear theoretical results (the small amplitude wave theoretical results). The second-order and the third-order solutions describe the nonlinear modification and the nonlinear interactions. The nonlinear impact appears not only in the n (n≥2) times’ high frequency components, but also in the low frequency components. It is also noted that the wave velocity depends on the wave number, depth, wave amplitude and surface tension.
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