This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodyn...The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection char...-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.展开更多
The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a ...The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.展开更多
Dynamic and numerical methods are used to discuss the atmospheric response to SST thermal forcing. The results show that for planetary scale systems, the standing SST thermal forcing can quickly excite a stable atmosp...Dynamic and numerical methods are used to discuss the atmospheric response to SST thermal forcing. The results show that for planetary scale systems, the standing SST thermal forcing can quickly excite a stable atmospheric equilibrium state response, which is characterized by obvious large-scale teleconnection oscillation in east-west and south-north directions. For synoptic scale systems, the SST thermal forcing mainly excites the atmospheric low-frequency oscillation. Some basic relation and dynamic processes between SST thermal forcing and atmospheric response pattern are revealed and some new viewpoints are presented.展开更多
Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the fl...Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.展开更多
Wave equation wave field numerical modeling technology is applied to the observation that deep layer imaging is difficult below a screening layer of high-velocity basalt. Three simple high-velocity basalt models are d...Wave equation wave field numerical modeling technology is applied to the observation that deep layer imaging is difficult below a screening layer of high-velocity basalt. Three simple high-velocity basalt models are designed on the basis of basalt formation characteristics. The analysis of deep-layer reflection seismic signal energy shows that lowfrequency seismic signals are capable of both penetrating the thin high-velocity basalt layer and reducing the diffraction noise caused by the rough surfaces. The simulation experiment of a complete 2D basalt model confirms that the low-frequency signals can be used to boost the quality of deep-layer imaging under the high-velocity basalt layer and achieve good results in low-pass filter processing of actual data.展开更多
A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exteri...A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.展开更多
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reyn...The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.展开更多
So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the...So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.展开更多
A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porou...A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.展开更多
This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes seco...This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.展开更多
To realize the application of the floating offshore wind turbine(FOWT)from deep to relatively shallow waters,a new concept of multi-column floating wind turbine platform with low center of gravity(CG)is designed and v...To realize the application of the floating offshore wind turbine(FOWT)from deep to relatively shallow waters,a new concept of multi-column floating wind turbine platform with low center of gravity(CG)is designed and validated.The multi-column low CG platform is designed to support a 6MW wind turbine class and operated at a water depth of 50m in the South China Sea.The frequency domain software WADAM and time domain software NREL-FAST are used to simulate coupled dynamic responses of the floating wind turbine system with second-order wave loads considering.The dynamic behaviors of multi-column low CG FOWT system under normal operation and parked conditions are presented.The influence of second-order wave force on the motion responses of the multi-column platform,fore-aft force and moment of the tower base and mooring force are researched respectively.The results demonstrate that the coupled dynamic responses at rated operating condition and extreme condition meet the normal operating requirements and extreme survival requirements of FOWT system in the shallow water(50m)of South China Sea.In addition,it is found that,the wave frequency response gradually replaces the second-order low frequency response as the main influencing factor of the coupled dynamic response of the FOWT system with the increasing severity of the sea states.However,in general,the magnitude of second-order low frequency response increases with the increasing severity of the design load case.Thus,in the subsequent design of the shallow water FOWT system,the second-order effects should be paid enough attention.展开更多
In the mid 20th century, great efforts were made to investigate the formation process of high-latitude cold vortex, which is regarded as a major weather system in the atmospheric circulation. In the late 1970s, Chines...In the mid 20th century, great efforts were made to investigate the formation process of high-latitude cold vortex, which is regarded as a major weather system in the atmospheric circulation. In the late 1970s, Chinese researchers noticed that the Northeast China cold vortex （NECV） is an active and frequently occurring weather system over Northeast Asia, which is generated under specific conditions of topography and land-sea thermal contrast on the local and regional scales. Thereby, the NECV study was broadened to include synoptic situations, mesoscale and dynamic features, the heavy rain process, etc. Since the 21st century, in the context of the global warming, more attention has been paid to studies of the mechanisms that cause the NECV variations during spring and early summer as well as the climatic impacts of the NECV system. Note that the NECV activity, frequent or not, not only affects local temperature and precipitation anomalies, but also regulates the amount of precipitation over northern China, the Huai River basin, and the middle and lower reaches of Yangtze River. The NECV influence can even reach the Guangdon~ Guangxi region. However, compared to the achievements for the blocking system study, theoretical studies with regard to the NECV system are still insufficient. Research activities regarding the mechanisms for the NECV formation, particularly theoretical studies using linear or weak nonlinear methods need to be strengthened in the future. Meanwhile, great efforts should be made to deepen our understanding of the relations of the NECV system to the oceanic thermal forcing, the low-frequency atmospheric variations over mid-high latitudes, and the global warming.展开更多
A simple analytical model is developed to interview the general features of the estuarine responses induced both by ocean tides and by low-frequency coastal fluctuations and wind forcings.Model estuary is assumed idea...A simple analytical model is developed to interview the general features of the estuarine responses induced both by ocean tides and by low-frequency coastal fluctuations and wind forcings.Model estuary is assumed ideally with constant depth and linearly varying breadth.The results indicate that the effects of bottom friction coefficient,the water depth and the breadth variation parameter on the estuarine response field virtually reflect the difference of the energy accumulation,transformation and dissipation in estuaries,It is found by comparison that there are obvious differences between tidally-induced and low-frequency forcing induced estuarine variations.For tidal response,bottom friction is a very important factor to affect the response magnitude,while for low-frequency response this effect becomes negligible.Thus a more simplified model for low-frequency estuarine response is produced,which gives more straightforward view to the response characteristics.Moreover,from the model solutions we deduce a general qualification for the estuarine resonance and discuss the relation between the resonance frequency and the estuarine geometry.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金National Natural Science Foundation of China under Grant Nos.51622803 and 51708064the National Key Research and Development Program of China under Grant No.2016YFE0200100
文摘The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
文摘-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.
基金funded by the National Natural Science Foundation of China(No.51809135)the Shandong Provincial Natural Science Foundation(No.ZR2018BEE 047)+1 种基金the National Natural Science Foundation of China–Shandong Joint Fund(No.U2006229)the SKL of HESS(No.HESS-1808).
文摘The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.
基金Foundation for Backbone Teachers in Higher Colleges of Education Ministry Natural Sci-ence Foundation of China (49975012)
文摘Dynamic and numerical methods are used to discuss the atmospheric response to SST thermal forcing. The results show that for planetary scale systems, the standing SST thermal forcing can quickly excite a stable atmospheric equilibrium state response, which is characterized by obvious large-scale teleconnection oscillation in east-west and south-north directions. For synoptic scale systems, the SST thermal forcing mainly excites the atmospheric low-frequency oscillation. Some basic relation and dynamic processes between SST thermal forcing and atmospheric response pattern are revealed and some new viewpoints are presented.
文摘Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.
文摘Wave equation wave field numerical modeling technology is applied to the observation that deep layer imaging is difficult below a screening layer of high-velocity basalt. Three simple high-velocity basalt models are designed on the basis of basalt formation characteristics. The analysis of deep-layer reflection seismic signal energy shows that lowfrequency seismic signals are capable of both penetrating the thin high-velocity basalt layer and reducing the diffraction noise caused by the rough surfaces. The simulation experiment of a complete 2D basalt model confirms that the low-frequency signals can be used to boost the quality of deep-layer imaging under the high-velocity basalt layer and achieve good results in low-pass filter processing of actual data.
文摘A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.
文摘The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.
文摘So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.
基金Project supported by the Major State Basic Research Development Program of China(No.G19990328)the National Natural Science Foundation of China(Nos.10771124,10372052,and 11101244)+2 种基金the National Tackling Key Problems Program of China(Nos.2011ZX05011-004,2011ZX05052,and 2005020069)the Doctorate Foundation of the Ministry of Education of China(No.20030422047)the Natural Science Foundation of Shandong Province of China(No.ZR2011AM015)
文摘A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.
文摘This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.
基金support from the National Natural Science Foundation of China (No.51809170 and No.12102210)State Key Laboratory of Ocean Engi-neering (No.GKZD010081)Programfor International Coopera-tion of Shanghai Science and Technology (No.18160744000).
文摘To realize the application of the floating offshore wind turbine(FOWT)from deep to relatively shallow waters,a new concept of multi-column floating wind turbine platform with low center of gravity(CG)is designed and validated.The multi-column low CG platform is designed to support a 6MW wind turbine class and operated at a water depth of 50m in the South China Sea.The frequency domain software WADAM and time domain software NREL-FAST are used to simulate coupled dynamic responses of the floating wind turbine system with second-order wave loads considering.The dynamic behaviors of multi-column low CG FOWT system under normal operation and parked conditions are presented.The influence of second-order wave force on the motion responses of the multi-column platform,fore-aft force and moment of the tower base and mooring force are researched respectively.The results demonstrate that the coupled dynamic responses at rated operating condition and extreme condition meet the normal operating requirements and extreme survival requirements of FOWT system in the shallow water(50m)of South China Sea.In addition,it is found that,the wave frequency response gradually replaces the second-order low frequency response as the main influencing factor of the coupled dynamic response of the FOWT system with the increasing severity of the sea states.However,in general,the magnitude of second-order low frequency response increases with the increasing severity of the design load case.Thus,in the subsequent design of the shallow water FOWT system,the second-order effects should be paid enough attention.
基金Supported by the National Natural Science Foundation of China(41630424,41275096,41175083,41305059,and 41405094)China Meteorological Administration Special Public Welfare Research Fund(GYHY201106016 and GYHY201006020)
文摘In the mid 20th century, great efforts were made to investigate the formation process of high-latitude cold vortex, which is regarded as a major weather system in the atmospheric circulation. In the late 1970s, Chinese researchers noticed that the Northeast China cold vortex （NECV） is an active and frequently occurring weather system over Northeast Asia, which is generated under specific conditions of topography and land-sea thermal contrast on the local and regional scales. Thereby, the NECV study was broadened to include synoptic situations, mesoscale and dynamic features, the heavy rain process, etc. Since the 21st century, in the context of the global warming, more attention has been paid to studies of the mechanisms that cause the NECV variations during spring and early summer as well as the climatic impacts of the NECV system. Note that the NECV activity, frequent or not, not only affects local temperature and precipitation anomalies, but also regulates the amount of precipitation over northern China, the Huai River basin, and the middle and lower reaches of Yangtze River. The NECV influence can even reach the Guangdon~ Guangxi region. However, compared to the achievements for the blocking system study, theoretical studies with regard to the NECV system are still insufficient. Research activities regarding the mechanisms for the NECV formation, particularly theoretical studies using linear or weak nonlinear methods need to be strengthened in the future. Meanwhile, great efforts should be made to deepen our understanding of the relations of the NECV system to the oceanic thermal forcing, the low-frequency atmospheric variations over mid-high latitudes, and the global warming.
文摘A simple analytical model is developed to interview the general features of the estuarine responses induced both by ocean tides and by low-frequency coastal fluctuations and wind forcings.Model estuary is assumed ideally with constant depth and linearly varying breadth.The results indicate that the effects of bottom friction coefficient,the water depth and the breadth variation parameter on the estuarine response field virtually reflect the difference of the energy accumulation,transformation and dissipation in estuaries,It is found by comparison that there are obvious differences between tidally-induced and low-frequency forcing induced estuarine variations.For tidal response,bottom friction is a very important factor to affect the response magnitude,while for low-frequency response this effect becomes negligible.Thus a more simplified model for low-frequency estuarine response is produced,which gives more straightforward view to the response characteristics.Moreover,from the model solutions we deduce a general qualification for the estuarine resonance and discuss the relation between the resonance frequency and the estuarine geometry.
