FREE-SURFACE EFFECTS ON A YAWED SURFACE-PIERCING PLATE

Analytical and experimental results are presented for a thin vertical surface-piercing plate, moving in the plane of the free surface with constant velocity at a small angle of attack. The analytical development is a generalisation of linear thin-wing theory, using a normal dipole distribution on the plate and in the wake downstream of the trailing edge. A Kutta condition is imposed at the trailing edge. The linear free-surface boundary condition and far-field condition are satisfied by using for the dipole potential the transverse derivative of the classical ship-wave Green function for steady forward motion. Computations are performed for a rectangular planform with aspect ratio 0.5, and these are compared with experimental data. Results are presented for the integrated force and moment, distributed pressure, strength of the leading-edge singularity, and profile of the free surface alongside the plate. Attention is focused on a local nonuniformity at the intersection of the free surface and trailing edge. The numerical solution is not convergent at this point, with the Kutta condition imposed. Experiments are made to study this region. These show that there is a jump in the free surface across the wake behind the trailing edge, contrary to the assumed boundary conditions, but this jump exists only above a critical Froude number. The jump is accompanied by a sharp transverse flow, contrary to the Kutta condition.