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Study on Wave Dissipation of the Structure Combined by Baffle and Submerged Breakwater 被引量:4
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作者 JU Lie-hong zuo Qi-hua +1 位作者 TENG Ling WANG Xing-gang 《China Ocean Engineering》 SCIE EI CSCD 2017年第6期674-682,共9页
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 c... 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 SCBSB 1 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. 展开更多
关键词 combined wave dissipation structure eigenfunction method physical model experiment transmissioncoefficient correction wave dissipation effect
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Improvement and application of a saturation based wave dissipation function in SWAN model 被引量:3
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作者 WANG Yi JIANG Xingwei 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2012年第1期24-32,共9页
Wave dissipation characteristics in SWAN (Simulating Waves Nearshore) model are investigated through numerical experiments. It is found that neither the fully developed integral parameters of wind waves (significan... Wave dissipation characteristics in SWAN (Simulating Waves Nearshore) model are investigated through numerical experiments. It is found that neither the fully developed integral parameters of wind waves (significant wave height and peak frequency) nor the high frequency spectral tail can be well reproduced by the default wave dissipation source terms. A new spectral dissipation source term is proposed, which comprises saturation based dissipation above two times of peak frequency and improved whitecapping dissipation at lower frequency spectrum. The reciprocal wave age (u./ep) is involved into the whitecapping model to adjust dissipation rate at different wind speed. The Phillips higher frequency saturation parameter in the saturation-based dissipation is no longer taken as a constant, but varies with wave age. Numerical validations demonstrate that both the wind wave generation process and higher frequency spectrum of wind waves can be well simulated by the new wave dissipation term. 展开更多
关键词 wind wave dissipation higher frequency spectrum SWAN
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Effects of wind input and wave dissipation formulations on the steady Ekman current solution
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作者 徐俊丽 宋金宝 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2014年第3期709-719,共11页
The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered: one from the wave modeling(WAM) program proposed by Hasselmann... The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered: one from the wave modeling(WAM) program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modifi ed Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profi le Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profi le Parameterization scheme agrees best with observations. 展开更多
关键词 Combi spectrum Stokes drift wind input wave dissipation steady Ekman current solution
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A SPECIAL SOLUTION OF WAVE DISSIPATION BY FINITE POROUS PLATES
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作者 王晋军 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第4期353-357,共5页
The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth... The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found that when the dimensionless porous-effect parameter G0 is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude. 展开更多
关键词 wave motion small-amplitude wave linear wave incident wave wave dissipation porous plates
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Hydraulic Design Method of Wave Dissipating Structure with Partially Perforated Front Wall 被引量:6
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《China Ocean Engineering》 SCIE EI 1995年第1期73-82,共10页
Based on the matching conditions of different fluid regions, the eigenfunction expansion method is used to develop a theoretical formula for wave reflection in front of the perforated structure with a partially slit f... Based on the matching conditions of different fluid regions, the eigenfunction expansion method is used to develop a theoretical formula for wave reflection in front of the perforated structure with a partially slit front wall. The accuracy of the solution is verified by comparing the numerical results with experimental data. In addition, a new hydraulic design method is developed by derivation of the theoretical formula with respect to the porosity of the slit wall, and the results of this design method is drafted for harbour engineers to use. 展开更多
关键词 wave dissipating structure hydraulic design method
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Hydrodynamic Performance of Vertical Porous Structures Under Regular Waves 被引量:2
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作者 A.S.Koraim O.S.Rageh 《China Ocean Engineering》 SCIE EI CSCD 2013年第4期451-468,共18页
The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission... The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission (kt), reflection (kr) and energy dissipation (ka) coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient (kt) decreases with the increase of the relative water depth (h/L), the wave steepness (Hi^L), the relative breakwater widths (B/L, B/h), the relative breakwater height (D/h), and the breakwater porosity (n). The reflection coefficient (kr) takes the opposite trend of kt when D/h=l.25 and it decreases with the increasing h/L, HJL and B/L when D/h〈1.0. The dissipation coefficient (kd) increases with the increasing h/L, HilL and B/L when D/h〈_l.O and it decreases when D/h=l.25. In which, it is possible to achieve values ofkt smaller than 0.3, k~ larger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L〉0.22, B/L〉O. 13, and H/L 〉0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained. 展开更多
关键词 water waves porous breakwaters wave attenuation wave transmission wave reflection wave dissipation
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Experimental Research on Wave Transmission over Submerged Rubble-Mound Breakwaters 被引量:2
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作者 左其华 Valeri PENCHEV +2 位作者 李鹏 Dorina DRAGANCHEVA 王登婷 《China Ocean Engineering》 SCIE EI 2008年第4期575-584,共10页
This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a tw... This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional (2D) model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed. 展开更多
关键词 submerged rubble breakwater wave transmission coefficient wave dissipation laboratory experiment
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Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions 被引量:2
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作者 郑永红 邱大洪 沈永明 《China Ocean Engineering》 SCIE EI 2001年第1期15-23,共9页
Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and the... Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set- up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions. 展开更多
关键词 wave energy dissipation wave set-up wave height associated with breaking mathematical model numerical simulation
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Interaction Between Waves and An Array of Floating Porous Circular Cylinders
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作者 赵芬芳 KINOSHITA Takeshi +3 位作者 鲍伟光 黄六一 梁振林 万荣 《China Ocean Engineering》 SCIE EI 2012年第3期397-412,共16页
The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory. To ... The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory. To design more effective floating breakwaters, the transmission rate of waves propagating through the array is evaluated. Each cylinder in the array is partly made of porous materials. Specifically, it possesses a porous sidewall and an impermeable bottom. In addition, an inner porous plate is horizontally fixed inside the cylinders. It dissipates the wave more effectively and eliminates the sloshing phenomenon. The approach suggested by Kagemoto and Yue (1986) is adopted to solve the multiple-scatter problem, while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies, which efficiently saves computation time. Meanwhile, a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results. The draft of the cylinders, the location of the inner porous plate, and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation. 展开更多
关键词 porous cylinders hydrodynamic interaction transmission rate open-area ratio wave dissipation
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Modelling windwave driven by typhoon Chan-Hom (201509) in the East China Sea
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作者 H.Q.Zhang B.C.Nie 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2016年第6期297-301,共5页
Typhoon-generated waves pose a serious threat to the development of offshore wind power; therefore typical wave parameters caused by typhoon near Donghai Bridge, a demonstration area of offshore wind farm, were analys... Typhoon-generated waves pose a serious threat to the development of offshore wind power; therefore typical wave parameters caused by typhoon near Donghai Bridge, a demonstration area of offshore wind farm, were analysed. We pay particular attention to the dissipation term which is one of the source terms of governing equation for windwave evolution in WAVEWATCH llI. Anisotropic energy dissipation in the wave propagation direction is considered and further applied in our model. A good agreement is observed by comparison with in situ data. Furthermore, the new improved model is used to simulate and forecast wave evolution caused by Chan-Hom (201509). The evolution of typical wave parameters i.e. significant wave height and mean wave period were discussed in the East China Sea, especially near Donghai Bridge. 展开更多
关键词 Windwave wave dissipation Saturation spectrum Significant wave height TYPHOON
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Hydrodynamic Coefficient Investigation on a Partial Permeable Stepped Breakwater Under Regular Waves
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作者 YIN Zegao ZHENG Zihan +1 位作者 YU Ning WANG Haojian 《Journal of Ocean University of China》 SCIE CAS CSCD 2021年第6期1341-1352,共12页
Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open ... Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open seawater and an inside harbor.Consequently,a partially permeable stepped breakwater(PPSB)is proposed to ensure safety and good water exchange capacity for an inside harbor,and a 3-D computational fluid dynamics(CFD)mathematical model was used to investigate the hydrodynamic coefficients using Reynolds-Averaged Navier-Stokes equations,Re-Normalization Group(RNG)k-εequations,and the VOF technique.A series of experiments are conducted to measure the wave heights for validating the mathematical model,and a series of dimensionless parameters considering wave and PPSB effects were presented to assess their relationships with hydrodynamic coefficients,respectively.With the increase in the reciprocal value of PPSB slope,incident wave steepness and permeable ratio below still water level(SWL),the wave reflection coefficient decreases.The wave transmission coefficient decreases with an increase in the reciprocal value of the PPSB slope and incident wave steepness;however,it increases with the increase in the permeable ratio below SWL.With increases in the reciprocal value of the PPSB slope,permeable ratio below SWL and incident wave steepness for relatively high wave period scenarios,the wave energy dissipation coefficient increases;however,it decreases slightly with increases in the incident wave steepness for the smallest wave period scenarios.Furthermore,simple prediction formulas are conducted for predicting the hydrodynamic coefficients and they are well validated with the related data. 展开更多
关键词 regular waves partially permeable stepped breakwater wave reflection coefficient wave transmission coefficient wave energy dissipation coefficient mathematical model
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Comparing Solutions to the Nonlinear Dissipative Wave Equation
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作者 Zaki Mrzog Alaofi Talaat Sayed El-Danaf Silvestru Sever Dragomir 《Journal of Applied Mathematics and Physics》 2022年第4期1281-1296,共16页
In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One of these non... In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One of these nonlinear partial differential equations, the dissipative wave equation, has been found to have a plethora of useful applications in different fields. A special class of solutions has been studied for the dissipative wave equation including exact solutions and approximate solutions. The aim of this article is to compare the non-polynomial spline method and the cubic B-spline method with the solution of a nonlinear dissipative wave equation. We will conduct a comparison of the stability of the two methods using the Von Neumann stability analysis. In addition, a numerical example will be presented to illustrate the accuracy of these methods. 展开更多
关键词 Dissipative wave Equation Cubic B-Spline Non-Polynomial Spline Truncation Error Von Neumann Stability
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Dissipative Effects of an Isolated Bubble in Water on the Sound Wave
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作者 黄景泉 李福新 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第6期579-584,共6页
The dissipative mechanisms of an isolated bubble in water for sound wave are analysed on the basis of the linearized theory of oseillations of a gas bubble.It isshown that the dissipative effects are obvious and conta... The dissipative mechanisms of an isolated bubble in water for sound wave are analysed on the basis of the linearized theory of oseillations of a gas bubble.It isshown that the dissipative effects are obvious and contain the scattering and absorptionof sound by a bubble the heat conduction is decisive in the dissipative effects of bu-bble;and the dissipative effects are maximum at resonance. 展开更多
关键词 scattering of bubble. absorption of bubble. dissipative on thesound wave
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Characteristics of dust acoustic waves in dissipative dusty plasma in the presence of trapped electrons
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作者 Ranjit K KALITA Manoj K DEKA +1 位作者 Apul N DEV Jnanjyoti SARMA 《Plasma Science and Technology》 SCIE EI CAS CSCD 2017年第5期21-28,共8页
The formation and propagation of nonlinear dust acoustic waves(DAWs) as solitary and solitary/shock waves in an unmagnetized, homogeneous, dissipative and collisionless dusty plasma comprising negatively charged mic... The formation and propagation of nonlinear dust acoustic waves(DAWs) as solitary and solitary/shock waves in an unmagnetized, homogeneous, dissipative and collisionless dusty plasma comprising negatively charged micron sized dust grains in the presence of free and trapped electrons with singly charged non-thermal positive ions is discussed in detail. The evolution characteristics of the solitary and shock waves are studied by deriving a modified Korteweg–de Vries–Burgers(mKdV–Burgers) equation using the reductive perturbation method. The mKdV–Burgers equation is solved considering the presence(absence) of dissipation. In the absence of dissipation the system admits a solitary wave solution, whereas in the presence of dissipation the system admits shock waves(both monotonic and oscillatory) as well as a combination of solitary and shock wave solutions. Standard methods of solving the evolution equation of shock(solitary) waves are used. The results are discussed numerically using standard values of plasma parameters. The findings may be useful for better understanding of formation and propagation of waves in astrophysical plasma. 展开更多
关键词 dust acoustic shock wave trapped electrons dissipation
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Experimental Study on Rectangular Floating Breakwaters 被引量:1
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作者 Yao Guoquan Ma Zhixiong Ding Bingcan Prof. Senior Engineer, River and Harbour Department, Nanjing Hydraulic Research Institute, Nanjing 210024 Senior Engineer, River and Harbour Department, Nanjing Hydraulic Research Institute, Nanjing 210024 Engineer, River and Harbour Department, Nanjing Hydraulic Research Institute, Nanjing 210024 《China Ocean Engineering》 SCIE EI 1993年第3期323-332,共10页
This paper proposes ten types of improved floating breakwaters for experiment with regular waves, based on the experience in the development and manufacture of existing floating breakwaters both at home and abroad, an... This paper proposes ten types of improved floating breakwaters for experiment with regular waves, based on the experience in the development and manufacture of existing floating breakwaters both at home and abroad, and on the results of experimental studies on the hydraulic characteristics of several types of floating breakwaters. The wave heights before and behind the breakwaters are measured, the movements of floating breakwaters are observed and the chain forces of the floating breakwaters are measured. The paper studies and compares the hydraulic characteristics of the improved rectangular floating breakwaters of which the internal and external structures and their installation methods are changed. Finally the optimal type of structure is selected through experiments. 展开更多
关键词 floating breakwater experimental study wave dissipation hydraulic characteristics
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Experimental Study of Mooring Type Effect on the Hydrodynamic Characteristics of VLFS
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作者 FENG Ming-wei SUN Zhao-chen +4 位作者 LIANG Shu-xiu LI Zhi LV Xuan JIA Song-lin HUXin-yue 《China Ocean Engineering》 SCIE EI CSCD 2022年第1期155-166,共12页
Mooring system is a significant part of very large offshore floating structures(VLFS).In this paper,a single module pontoon type VLFS model considering four mooring types is studied through physical model tests to det... Mooring system is a significant part of very large offshore floating structures(VLFS).In this paper,a single module pontoon type VLFS model considering four mooring types is studied through physical model tests to determine the effects of mooring conditions on the hydroelastic response,mooring force,incident coefficient,reflection coefficient and energy dissipation coefficient.Eight mooring cables are symmetrically arranged on both sides of the model.The floating body model satisfies the similarity of stiffness and gravity,while the cable satisfies the similarity of elasticity and gravity.The results show that the effect of mooring type on mooring force is greater than that on hydroelastic response.Increasing the initial tension of the mooring cable will reduce the amplitude of the leeward of the VLFS model.The mooring angle of the mooring cable will affect the maximum mooring force and the initial tension of the mooring line will affect the wave period in which the maximum mooring force occurs.The transmission coefficient and wave energy dissipation coefficient will change regularly with different mooring types.These results may provide a reference to facilitate the mooring design of VLFS. 展开更多
关键词 VLFS hydroelastic response mooring system 3D experimental test mooring force wave reflection coefficient wave transmission coefficient wave dissipation coefficient
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A LINEARLY-FITTED CONSERVATIVE (DISSIPATIVE) SCHEME FOR EFFICIENTLY SOLVING CONSERVATIVE (DISSIPATIVE) NONLINEAR WAVE PDES 被引量:1
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作者 Kai Liu XinyuanWu Wei Shi 《Journal of Computational Mathematics》 SCIE CSCD 2017年第6期780-800,共21页
The extended discrete gradient method is an extension of traditional discrete gradient method, which is specially designed to solve oscillatory Hamiltonian systems efficiently while preserving their energy exactly. In... The extended discrete gradient method is an extension of traditional discrete gradient method, which is specially designed to solve oscillatory Hamiltonian systems efficiently while preserving their energy exactly. In this paper, based on the extended discrete gradient method, we present an efficient approach to devising novel schemes for numerically solving conservative (dissipative) nonlinear wave partial differential equations. The new scheme can preserve the energy exactly for conservative wave equations. With a minor remedy to the extended discrete gradient method, the new scheme is applicable to dissipative wave equations. Moreover, it can preserve the dissipation structure for the dissipative wave equation as well. Another important property of the new scheme is that it is linearly-fitted, which guarantees much fast convergence for the fixed-point iteration which is required by an energy-preserving integrator. The efficiency of the new scheme is demonstrated by some numerical examples. 展开更多
关键词 Conservative (dissipative) wave PDEs Structure-preserving algorithm Linearly-fitted Average Vector Field formula Sine-Gordon equation.
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Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity 被引量:6
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作者 谭雷 唐国强 +3 位作者 周忠兵 Liang Cheng Xiaobo Chen 吕林 《Journal of Hydrodynamics》 SCIE EI CSCD 2017年第5期805-816,共12页
A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The re... A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model(ε) and that devised for the modified potential flow model(μ_p) is established, namely, μ_p=3πεω_n/8 (where ω_n is the natural frequency). This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model. 展开更多
关键词 Water wave narrow gap fluid resonance energy dissipation artificial damping
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Oscillatory solution to semilinear dissipative wave equations
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《Chinese Science Bulletin》 SCIE CAS 1998年第9期787-788,共2页
关键词 wave MATH Oscillatory solution to semilinear dissipative wave equations
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Physiological Flow of Jeffrey Six Constant Fluid Model due to Ciliary Motion 被引量:1
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作者 A.Shaheen S.Hussain S.Nadeem 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第12期701-708,共8页
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ... The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number. 展开更多
关键词 ciliary motion metachronal wave Jeffrey six-constant fluid viscous dissipation effects and perturbation method
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