A full time-domain combined numerical model for evaluating the wave-induced motion response of a floating body in shallow water was set up in this paper. Comparing with other analogous models, it does not need to calculate the hydrodynamic coefficients and convolution integrals. The combined model includes the effects of the quay wall and the sea floor in a harbor on wave propagation and also takes account of shoaling, refraction and nonlinear wave-wave interaction. The numerical tests show that the present combined model is capable of calculating the motion of a floating body induced by shallow water nonlinear waves.


Predicting the wave-induced motion of a floating body in a harbor is a classical problem, and hard to be realized accurately. Compared to problem in the open and deep water, the effect of the quay walls and the sea floor on the wave transformation must be considered while analyzing the interaction between waves and a floating body in shallow water.

At first researchers used simple method and linear theory to deal with the problem and calculate the motion response of the floating body. Representative jobs include Sawaragi and Kubo (1982), Ohyama and Tsuchida (1997), Kubo and Sakakibara (1997), and Weiler and Dekker (2003). The method of Sawaragi and Kubo (1982) divided the whole water area into three parts:

  1. the region outside the harbor;

  2. the region inside the basin;

  3. the region underneath the floating body.

The wave field in each region was calculated separately by linear theory while keeping the velocity and the velocity potential continuous at the boundaries between these regions. Ohyama and Tsuchida (1997) improved the method for the harbor with an arbitrary shape and uneven bottom. The computational domain was also divided into different regions, and the wave field was also calculated through linear theory. Kubo and Sakakibara (1997) developed a method to take into account both the low-frequency harbor oscillations and the short waves. The short waves were considered as progressive waves while the longer waves were considered as standing waves. In order to consider the presence of the quay walls, Weiler and Dekker (2003) took the standing waves as two wave trains propagating in opposite directions.

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