Application of potential theory in calculating wave-induced vertical forces on horizontal cylinders near a plane boundary

Hydrodynamic forces acting on a horizontal cylinder located in the vicinity of the bottom are analyzed by a diffraction theory which solves the problem in terms of a velocity potential. The cylinder is assumed to be rigidly anchored to the bottom at a sufficient depth, so that it has no influence on the surface profile. The potential function φ is defined as the sum of the incident wave velocity potential φ w and the scattered wave velocity potential φa. The results of measurements of wave-induced pressures and forces on a horizontal cylinder located close to the bottom are compared with the theoretical solution based on the potential theory for incompressible, perfect fluid and ideal boundary conditions at the bottom and the surface of the cylinder. The experiments were carried out in the Large Wave Channel in Hannover with a cylinder of 0.8 m diameter. Thus the results are in a scale which corresponds to real pipelines. The analysis shows that the potential theory explains the components with double frequency of the wave in pressures and vertical forces as far as the amplitudes are concerned. In the experiments, the Keulegan-Carpenter number is rather low and the inertia hydrodynamic forces on the cylinder are dominant. It seems that the observed phase shift between the force component and the wave results from the energy dissipation which is not considered in the theoretical solution.