Abstract: In order to investigate the wave elevation on the free surface and the nonlinearity of a two dimensional tank with irrotational and inviscid fluid under segmented excitation, we utilize the Crank-Nicolson finite difference method for the potential flow equation. By changing the excitation parameters, we draw the wave height of the free surface under different excitation conditions. As shown in the numerical results, the wave elevation demonstrates the regular periodic beating phenomenon under the single horizontal excitation with different excited frequencies. Under the segmented excitation, the phenomenon of free surface wave beating disappears immediately when the horizontal excitation disappears. When the wave elevation of the free surface is small, the wave on the free surface exhibits the form of standing wave. When the free surface wave elevation is large, the wave crest and trough decrease, and the nonlinear phenomenon occurs. In addition, when the amplitude of the wave becomes larger, the nonlinear phenomenon is more obvious.

Key words: potential flow equation, Crank-Nicolson finite difference method, segmented excitation, free surface elevation, nonlinear phenomenon