Journal of Ocean Engineering and Science

Volume 1, Issue 2

(1)A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

Qicheng Meng^∗, Chongwei Zhang
Department of Mechanical Engineering, University College London, London, UK
Received 26 August 2015; received in revised form 30 October 2015; accepted 30 November 2015
Available online 14 March 2016

Abstract
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.
© 2016 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Internal solitary waves; Rigid-lid two-layer model; Third-order KdV solution; Numerical wave tank; OpenFOAM; Waves2Foam.