A laboratory study of wave crest statistics and the role of directional spreading

Abstract

This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crestheight distributions.

The interaction between steep waves and a surface-piercing column

“…If the water surface is steep, but not sufficiently steep, the impact will be replaced by very large run-up velocities. Although recent research [28] has shown that large incident sea states will be steeper than is commonly predicted, with a higher than expected occurrence of wave breaking, this alone is not sufficient to explain the occurrence of wave impacts on the columns of some offshore structures. Indeed, both field observation and extensive model testing have shown that columns that are large, but not so large that they lie in the linear diffractions regime, are particularly susceptible to both wave impacts and large run-up velocities.…”

A laboratory study of nonlinear changes in the directionality of extreme seas

“…In this study, the appropriate weighting is based upon a normal distribution with a standard deviation of σ θ in accordance with the directional distribution outlined in equation (2.8). This method was previously adopted in [26,27] and formed the basis of the earlier laboratory study outlined in [6]. Given that this study is specifically concerned with the directionality of the sea state, the merits of these approaches need to be carefully considered.…”

“…Indeed, this study concerns a subset of four of these sea states, the details of which are given in table 2. The original data, full details of which are given in [6], concern time-histories of the water surface elevation, η ( t ), recorded over the working area of the wave basin. This study uses η ( t ) data recorded at one representative position, located 4.75 m downstream of the wave paddles.…”

“…In all cases, the random wave data, incorporating η ( t ), u ( t ) and v ( t ), were based upon 20 × 3 h simulations. Once again, the 3 h duration represents the equivalent ‘full-scale’ value based upon the scaling noted below and each simulation (or seed) involves a different set of random phases, amplitudes and directions; further details of the generated data are given in [6]. …”

High waves in Draupner seas—Part 1: numerical simulations and characterization of the seas

“…Beforehand, it can be argued that the effect of the Benjamin-Feir instability may be very mild, because the value of k D = 1.6 of the sea is just above the critical value 1.36, and the spreading is wide which could reduce the steepness as observed in extensive laboratory experiments of Latheef and Swan (2013). The steepness, which, for unidirectional waves, would give k Hs/2 = 0.14, turns out to be much larger, up to a factor 5, in the simulations near high crests.…”