A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system.The solution corrects an error by Mirie and Su(1984).A two-...A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system.The solution corrects an error by Mirie and Su(1984).A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam.Various analytical solutions,including the first-order to third-order KdV solutions,the eKdV solution and the MCC solution,have been used to initialise the flow fields in the CFD simulations of internal solitary waves.Two groups including 11 numerical cases have been carried out.In the same group,the initial wave amplitudes are the same but the implemented analytical solutions are different.The simulated wave profiles at different moments have been presented.The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively.It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases.The finding is significant for the further simulations involving internal solitary waves.展开更多
基金This work is supported by Lloyd’s Register Foundation(LRF)through the joint centre involving University College London,Shanghai Jiaotong University and Harbin Engineer-ing University,to which the authors are most grateful.Lloyd’s Register Foundation helps to protect life and property by sup-porting engineering-related education,public engagement and the application of researchThe first author acknowledges the scholarship sponsored by the Erasmus Mundus Europe Asia(EMEA)scholarship pro-gramme,Faculty of Engineering of University College Lon-don and the Henry Lester Trust LtdThe second author ac-knowledges the financial support by the China Scholarship Council(CSC)(no.201206680001).
文摘A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system.The solution corrects an error by Mirie and Su(1984).A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam.Various analytical solutions,including the first-order to third-order KdV solutions,the eKdV solution and the MCC solution,have been used to initialise the flow fields in the CFD simulations of internal solitary waves.Two groups including 11 numerical cases have been carried out.In the same group,the initial wave amplitudes are the same but the implemented analytical solutions are different.The simulated wave profiles at different moments have been presented.The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively.It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases.The finding is significant for the further simulations involving internal solitary waves.
