Run-up on a structure due to second-order waves and a current in a numerical wave tank

A numerical wave tank is considered in which the interaction between waves, current and a structure is simulated by a 3D boundary element model in the time domain. Through a Taylor series expansion and a perturbation procedure the model is formulated to second order in wave steepness and to first order in current speed. The boundary-value problem is separated into a known incident wave field and an unknown scattered wave field, the latter being absorbed at the radiation boundaries using active wave absorption. The present paper focuses on the wave run-up on a structure in waves and current. For the simulations a bottom mounted vertical circular cylinder is chosen. The numerical results show good agreement with previous analytical and numerical solutions for second-order wave diffraction without a current and first-order wave diffraction with a collinear current. The inclusion of a current in the calculation of second-order wave run-up is new and the validity of the results is demonstrated by a parametric study. It is shown that both the current and the second-order wave components are of significant importance in calculating magnitude and location of the maximum run-up on a structure.

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