On evaluation of wave forces and runups on cylindrical obstacles

A computational analysis of diffraction of water waves caused by large-diameter circular cylinder piercing the free surface is performed. With reference to linear-wave cases, the phenomenon is considered in terms of: i) velocity-potential theory, ii) numerical solution of the primitive-variable Euler equations, and iii) numerical solution of the primitive-variable full Navier–Stokes equations. It is found that, as for the values of the forces exerted by the wave on the cylinder, the results obtained from the numerical integration of the Euler equations and from the potential theory slightly underestimate those obtained from the numerical integration of the Navier–Stokes equations (and also from experimental results obtained by other authors), while both the potential theory and Euler equations results strongly underestimate the values of the runups on the cylinder as compared with the Navier–Stokes equations results (and also with the experimental results obtained by other authors). Thus, new concise expressions for evaluating both forces and runups are proposed.