In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of...In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.展开更多
Tsunamis have a severe impact on marine coastal structures.Tsunami is generally simplified as solitary wave as they propagate,and the presence of the aftermath of Tsunami is similar to a second solitary wave.Waveform ...Tsunamis have a severe impact on marine coastal structures.Tsunami is generally simplified as solitary wave as they propagate,and the presence of the aftermath of Tsunami is similar to a second solitary wave.Waveform evolution occurs as solitary wave propagate down a gentle slope.This paper reveals the propagation of double solitary waves and slope climbing by numerical simulation where the prototype of the embankment is around Shantou city in the Guangdong Province,China.It not only enriches the theory of solitary wave,but also has important implications for the analysis of tsunami disaster mechanism and the hydrodynamic load characteristics of structures.Based on the average Navier-Stokes equation and the VOF approach,numerical simulation results are given,including changes in the velocity field of the climbing and falling process species.The results show that the double solitary waves produce a strong reflux effect,which results in the second solitary wave climbing significantly less than the height of the first solitary wave without the influence of the current.At the same time,double solitary waves can have a much stronger effect on the embankment.展开更多
A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is pro- posed according to the ＇jalousie＇ control mode. A new wave-maker based on the princip...A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is pro- posed according to the ＇jalousie＇ control mode. A new wave-maker based on the principle was manufactured and the experi- ments on the generation and evolution of internal solitary wave were conducted. Both the validity of the new device and ap- plicability range of the KdV-type internal soliton theory were tested. Furthermore, a measurement technique of hydrodynamic load of internal waves was developed. By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank, their interaction characteristics were determined. It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement re- suits of internal wave forces are confirmed to be correct.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10771072, 10735030, and 90718041Shanghai Leading Academic Discipline Project under Grant No.B412
文摘In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.
基金supported by Comprehensive Geological Survey of Chaoshan Coastal Zone (No. DD20208013)
文摘Tsunamis have a severe impact on marine coastal structures.Tsunami is generally simplified as solitary wave as they propagate,and the presence of the aftermath of Tsunami is similar to a second solitary wave.Waveform evolution occurs as solitary wave propagate down a gentle slope.This paper reveals the propagation of double solitary waves and slope climbing by numerical simulation where the prototype of the embankment is around Shantou city in the Guangdong Province,China.It not only enriches the theory of solitary wave,but also has important implications for the analysis of tsunami disaster mechanism and the hydrodynamic load characteristics of structures.Based on the average Navier-Stokes equation and the VOF approach,numerical simulation results are given,including changes in the velocity field of the climbing and falling process species.The results show that the double solitary waves produce a strong reflux effect,which results in the second solitary wave climbing significantly less than the height of the first solitary wave without the influence of the current.At the same time,double solitary waves can have a much stronger effect on the embankment.
基金supported by the National Natural Science Foundation of China(Grant No.11072267)the National High Technology Research and Development Program of China(Grant No.2008AA09Z316)the Pre-Research Foundation of PLA University of Science&Technology(Grant No.KYLYZLXY1202)
文摘A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is pro- posed according to the ＇jalousie＇ control mode. A new wave-maker based on the principle was manufactured and the experi- ments on the generation and evolution of internal solitary wave were conducted. Both the validity of the new device and ap- plicability range of the KdV-type internal soliton theory were tested. Furthermore, a measurement technique of hydrodynamic load of internal waves was developed. By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank, their interaction characteristics were determined. It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement re- suits of internal wave forces are confirmed to be correct.
