Abstract
A study of the Boussinesq equations for waves propagating from deep water to shallow water is presented. In this paper, we derive the O(μ6) Boussinesq equations with the recursion forms not only for main variables but also coefficients. This greatly reduces the efforts needed to derive the higher‐order Boussinesq equations. Parameters concerning the linear and nonlinear wave properties are also derived to analyze the accuracy of present models. The linear properties include the phase velocity, the group velocity and the particle velocities. The forcing terms of the continuity equation and the equation of motion are developed to analyze the nonlinear properties. By choosing a suitable water‐depth parameter m, the optimal wave models are consequently determined. Our model provides an easier and more flexible method to analyze the wave mechanics than previous studies based on the Padé approximation.
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