Numerical study of superposition principle for surface gravity waves

Abstract

The study of surface gravity wave is very important for the safety of marine vessels and the design of coastal and offshore structures. Gravity-induced sea waves mostly show a nonlinear behaviour, but at a low wave steepness, these waves can be approximated as linear waves and superposition principles can be applied. Various wave phenomena such as standing waves, constructive and destructive interference, wave groups and generation of random waves are based on superposition principle. Random waves are generally modelled using wave spectrum, which is a representation of wave energy in the specified frequency range. Wave spectrum is broken into different wave components which are superposed to produce a random wave. In the present work, volume of fluid method is used for numerical simulation of surface gravity waves. Implicit formulation for volume fraction equation along with the bounded second order in time is used, which allows better temporal accuracy and numerical stability at larger time step size. The surface gravity wave is modelled by providing the wave profiles and velocities at upstream boundary. In the downstream, pressure outlet boundary is used for the specification of the hydrostatic pressure profile. Numerical beach zone is defined adjacent to the pressure outlet boundary to suppress the wave reflections propagating upstream. Random waves are modelled using JONSWAP spectrum. Formation of constructive and destructive interference, standing wave, wave pockets and modelling of random wave is achieved with numerical approach, and wave kinematics are validated against the analytical results.