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Publications
Mohapatra, S.C., Fonseca, R.B. and Guedes Soares, C. (2018), “Comparison of analytical and numerical simulations of long nonlinear internal solitary waves in shallow water”, Journal of Coastal Research, Vol. 34(4), pp. 928-938
This study compares the simulations of long nonlinear internal waves between analytical and numerical wave models in shallow water. In order to present the analytical solutions, a mathematical method based on travelling wave hypothesis is applied to obtain the exact solitary wave solutions of the generalized Gardner equation of any order. Further, the internal waves are demonstrated by analysing the solutions of the classical Gardner equation, Korteweg-de Vries equation, and modified Korteweg-de Vries equations. The shape and characteristics of the three-dimensional solitary waves are studied by analysing different numerical results of the explicit nonlinear analytical solutions. The Gardner equation (extended KdV equation) basically behaves with the same properties as the Boussinesq equations of travelling wave solutions in shallow water. The obtained analytical travelling wave solutions have been used in MIKE 21 BW numerical wave model to compare the internal solitary waves by imposing wave celerity and wave amplitudes in shallow water. The effect of different physical parameters and sign of nonlinearity on the internal solitary wave transformations in shallow water are analyzed. It is observed that the solution of the generalized Gardner equation is bell-profile solitary wave and the velocity profiles are very close to the numerical model. For all the cases, the patterns of internal solitary waves are similar in nature and their peak amplitudes are very close between analytical and numerical model solutions.
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