A comparative study between the IGN-2 equations and the fully nonlinear, weakly dispersive Boussinesq equations

作者：Zhao, B. B.; Duan, W. Y.^*; Demirbilek, Z.; Ertekin, R. C.; Webster, W. C.

来源：Coastal Engineering, 2016, 111: 60-69.

DOI：10.1016/j.coastaleng.2016.01.011

• Irrotational Green-Naghdi equations
• IGN-2 equations
• Boussinesq equations
• Steady water waves
• Nonlinear and weakly dispersive waves

This work focuses on the comparison between the fully nonlinear, and weakly dispersive Boussinesq equations and the irrotational Green-Naghdi Level 2 (IGN-2) equations for incompressible and inviscid fluid and irrotational flow resulting from waves in finite water depth. We provide in this paper for the first time a comprehensive comparison of the GN/IGN and Boussinesq wave theories for strongly nonlinear and weakly dispersive waves. The Boussinesq approach results in many different theories depending on the different orders of approximation of nonlinearity and dispersion used in the corresponding perturbation series. The fully nonlinear, weakly dispersive Boussinesq equations have been widely used in problems involving coastal regions and harbors because it is more efficient than fully nonlinear, strongly dispersive Boussinesq equations. A competing theory is the strongly nonlinear IGN-2 wave theory. Since both sets of equations have comparable complexity, it is appropriate to compare the results of these equations with known numerically exact solutions to determine the advantages of each approach. In this study, we use the same iterative algorithm to obtain the steady solutions of the IGN-2 and Boussinesq equations for periodic waves. The steady solutions of the IGN-2 and Boussinesq equations are studied for four different wavelengths that cover a range of applicability of the theories. We show in this study that the Boussinesq equations give more accurate results for the velocity distribution at the wave-crest transection. The IGN-2 equations give more accurate results for the velocity distribution at the wave-trough transection. Moreover, it is shown that the IGN-2 equations give more accurate results on the wave speed and wave profile, and that they can treat accurately waves higher than the ones that the Boussinesq equations can treat. The calculations show that both of these sets of equations are very good for strongly nonlinear wave simulations and the limitations of each are different.

• 出版日期2016-5
• 单位哈尔滨工程大学