Numerical calculations of large transient water waves

Abstract

This paper concerns the description of a two-dimensional irregular sea state in which a large transient wave is generated through the constructive interference (or focusing) of the component waves. A numerical model is presented and comparisons are made with recent laboratory data. This includes measurements of the horizontal kinematics within the crest to trough region. The proposed solution is based upon a Fourier series expansion in space and time, in which the amplitude of the individual harmonics are determined by a least squares fit to the non-linear free surface boundary conditions. This approach allows for a realistic mix of free waves (with differing phase velocities) and their associated bound waves. The solution, which is not assumed to be either locally or globally steady, can be used to predict the kinematics beneath a recorded (or predicted) water surface elevation. The numerical results are in excellent agreement with the laboratory data, and the solution is robust in the sense that convergence is always achieved from simple initial conditions. The proposed model is not computationally intensive and may thus be suitable for design calculations.