Comparison of Analytical and Numerical Simulations of Long Nonlinear Internal Solitary Waves in Shallow Water

This study compares the results of long nonlinear internal waves between analytical and numerical wave models in shallow water. To present the analytical solutions, the (G'/G) expansion method is applied to obtain the exact and explicit nonlinear solitary wave solutions of the generalized Gardner equation of any order in the presence of dispersive coefficient. The internal waves are demonstrated by analysing the solutions of the classical Gardner equation, modified Korteweg-de Vries equation, and Korteweg-de Vries equations from the generalized solution. The shape and characteristics of the three-dimensional solitary waves are studied by analysing different numerical results of the nonlinear analytical solutions. The Gardner equation basically behaves with the same properties as the Boussinesq equations of travelling wave solutions in shallow water. The present analytical results are compared with ones recently obtained to verify the accuracy of the peak amplitude of the velocity profiles. Then, the obtained analytical solutions have been used in the MIKE 21 BW numerical wave model to compare the internal solitary waves by imposing parametric values associated in wave speed of the solitary wave. The effects of sign of nonlinearities and dispersive coefficient on the internal solitary wave transformations are analyzed. The results show similar peak amplitudes between the present and ones recently obtained. Further, the present solution is step-profile solitary wave. The solitary wave amplitude of the analytical model is the equilibrium position of the wave displacement of the numerical model.