Analytical Method of Linear Viscous Water Wave Applied to Flap Type Wave-maker

Optimizing design to harbor and coastal structures for the purpose of working efficiently always depends on accurate analysis and simulation to the wave field. One of the essential analysis is the effect resulted by viscosity. However, most researches focus on numerical simulation instead of analytical solution. Moreover, the approximation of inviscid fluid to the analytical research might neglect the effect of interaction between solid boundary and fluid. In the assumption that the homogeneous fluid is incompressible, priodic and linearity, the small amplitude wave theory is adopted in the present study to investigate the wave field and physical mechanism of flap type wave-maker. First, the present study utilizes linearity to separate wave field into irrotational and rotational part and determines the governing equation and boundary condition. But, the equation could not be solved in one process because of including two variables. Hence, the present study proposes the two processes analytical method. It uses first guess process to solve two parts including only one varible, then applies iteration process to solve the whole problem. Second, the present study ultilizes vorticity-streamfunction equation to be the boundary conditions of vorticity and diffusion equation to analyze vorticity in the wave field. The reason is that there are no boundary conditions for calculation of vorticity. Thus, the present study takes identy of vorticity and streamfunction as the boundary conditions and analyzes the distribution of vorticity in the wave field successfully. The result indicates that the distribution of vorticity might decay along x direction, the effect of vorticity is confined near the wave-maker plate and might appear in the free surface and bottom which make up the questionable problem at endpoint. Furthermore, owing to considering the viscosity, boundary layer flow would appear near the boundary and causes the velocity distribution to be different from irrotaitonal wave field. Comparing viscid wave field with irrotation wave field, the two wave fields almost have the same behavior while vorticity would appear near the plate due to viscosity. At the bottom, viscid wave field has no-slip condition because of boundary layer flow. Due to the correct expression of vorticity distribution in the wave-maker, the present study is helpful in analysis of vorticity and experiments about wave-maker etc.