In this paper, the Homotopy Analysis Method (HAM) is applied to solve the fully nonlinear partial differential equation for the steady propagating periodic gravity wave of finite water depth. The series solution of the wave elevation and the velocity potential function are obtained. And then the velocity and pressure fields are plotted and discussed carefully. In order to overcome the drawback of the integral calculations with complex free surface elevation, the discrete integration and fitting procedure based on high-order Fourier series is developed. Based on the accurate HAM solution and fitting technique, the mass, momentum and energy conservation equations are validated. At last, the corresponding mean fluxes are calculated and the velocities of the mass transport and energy transport are supplied accurately.

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