EXTREME WAVES IN SHALLOW AND INTERMEDIATE WATER DEPTHS

This paper concerns the description of large transient waves in shallo w and intermediate water depths. It builds upon recent advances in the description of deep water waves, and provides the first quantitative comparisons with a new kinematic model which has hitherto only been va lidated in deep water conditions. A new series of experimental observa tions is presented in which the wave components within a random (or ir regular) sea state are focused to produce a large transient wave group . Comparisons with both linear and second-order solutions suggest that non-linear wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacen t wave troughs are broader and less deep. Spectral analysis of the mea sured water surface elevation suggest that in addition to the developm ent of significant long-wave energy, there is also a transfer of energ y to the shorter, high frequency, harmonics. This energy redistributio n has a significant effect upon the underlying kinematics. In particul ar, the near-bed velocities are shown to be in good agreement with the second-order solution which includes the long-wave (or frequency-diff erence terms) first identified by Longuet-Higgins and Stewart. Further more, the near-surface kinematics are shown to be highly non-linear. I ndeed, a linear wave theory, based upon a correct representation of th e freely propagating linear harmonics, is generally found to under-est imate the near-surface horizontal velocity. However, if the linear cal culations are based upon a measured wave spectrum, the kinematic predi ctions suffer from high frequency contamination and require empirical correction. In contrast, the non-linear numerical model presented by B aldock and Swan provides a good description of the measured kinematics over the entire water depth.