Analytic solution for flat-plate under a free surface with finite depth effects

In this study, the lift coefficient and wave deformations for a two-dimensional flat-plate in noncavitating condition were computed using a closed-form (analytic) solution. This plate moves at a constant speed beneath a free surface in water of finite depth. The model represents the flat-plate using a lumped vortex element within the constraints of potential flow theory. The kinematic and dynamic free surface conditions were combined and linearized. This linearized free surface condition was then applied to get the total velocity potential. The method of images was utilized to account for the effects of finite depth in the calculations. The lift coefficient of the flat-plate and wave elevations on the free surface were calculated using the closed-form solution. The lift coefficients derived from the present analytic solution were validated by comparing them with Plotkin