The second-order wave force on a vertical cylinder

The second-order wave force is analysed for diffraction of monochromatic water waves by a vertical cylinder. The force is evaluated directly from pressure integration over the cylinder, and the second-order potential is derived by Weber transformation of the corresponding forcing function on the free surface. This forcing function is reduced to a form which involves a simple factor inversely proportional to the radial coordinate plus an oscillatory function which decays more rapidly in the far field. This feature alleviates the slow rate of convergence involved in capturing the far-field effect. Benchmark computations are obtained and compared with other works. Asymptotic approximations are derived for long and short wavelengths. The analysis and results are primarily for the case of infinite fluid depth, but the finite-depth case is also considered to facilitate comparison with other computations and to illustrate the importance of finite-depth effects in the long-wavelength asymptotic regime.