This paper studies the dynamic interactions of the seabed motion with the free-surface flow by numerical calculation. The formulation of stream function and vorticity in an evolving boundary-fitted grid system supplies a comprehensive tool to analyze the transient flow phenomena with moving boundaries. The finite-analytic method with LSOR technique is used to calculate various configurations of fluid and sea-bed motion. The numerical result in the present study shows the interesting flow and wave characteristics caused by the sea-bed motion.
The instantaneous motion of the sea bed, caused by earthquakes, erosions or landslides, etc., sometimes generates complicate flow phenomena that are of great interests to both coastal engineers and scientific researchers. The strongly transient and nonlinear behaviors of fluid particles disturbed by the large and irregular sea-bed motion are usually difficult to be solved by analytical techniques. Moreover, the viscous effects on the nearby fluid flow may become significant at the initial stage of the bottom motion. The inclusion of viscosity in the formulation makes the problem more complicated but worthy to study. This paper intends to apply a numerical method to investigate the related flow phenomena due to the periodic sea-bed motion and analyzes their transient interactions with the nonlinearity and viscosity of fluid motion. The present study adapts the kinematic formulation of stream function and vorticity to find out the flow solution. Since the bounding geometry of the flow domain may vary with time, the evolving boundary-fitted grids should construct a better coordinate system in the numerical application [1, 2]. Through this grid specification, one can not only handle the irregular and moving boundaries directly but also control the grid density to resolve some flow regions as required, for example, near the solid surface.
