Second-order wave loading on a horizontal rectangular cylinder of substantial draught

Approximate first- and second-order analytical solutions of wave diffraction of a semi-submerged horizontal cylinder of rectangular cross-section are presented. The solutions are based on the assumption that the pressure in the fluid domain underneath the cylinder is linearly dependent on the horizontal space coordinate. Basically, this approach is valid when the clearance between the bottom of the cylinder and the sea bottom is small in comparison with the wave length and is recommended for a cylinder of substantial draught where due to the small clearance other methods are difficult to apply. Boundary conditions are satisfied by a choice of a proper form of the potential functions and by making use of the properties of matching conditions. Theoretical results reveal that the magnitude of the vertical second-order time-dependent loads could be significant and even exceed the corresponding first-order quantities. This phenomenon, which occurs even at moderate steepnesses, as well as the assumption of a linear pressure distribution, are confirmed by experiments performed in a wave tank.