Improved crest height predictions for nonlinear and breaking waves in large storms

The statistical distribution of zero-crossing crest heights represents a critical design input for a wide range of engineering applications. The present paper describes the development and validation of a new crest height model, suitable for application across a broad range of water depths. The purpose of this model is two-fold: first, to describe the amplifications of the largest crest heights arising due to nonlinear interactions beyond a second-order of wave steepness, and second, to incorporate the dissipative effects of wave breaking. Although these two effects act counter to each other, there is substantial evidence to suggest departures from existing models based upon weakly nonlinear second-order theory; the latter corresponding to current design practice. The proposed model has been developed based on a significant collection of experimental results and a small subset of field measurements. It incorporates effects arising at different orders of nonlinearity as well as wave breaking in a compact formulation and covers a wide range of met--ocean conditions. Importantly, the new model has been independently validated against a very extensive database of experimental and field measurements. Taken together, these include effective water depths ranging from shallow water (! ∼ 0.5) to deep water (! > 3) and sea-state steepnesses covering mild, severe and extreme conditions. The new model is shown to provide a significant improvement in crest height predictions over existing methods. This is particularly evident in the steepest, most severe sea--states which inevitably form the basis of design calculations

A new crest height distribution for nonlinear and breaking waves in varying water depths

The statistical distribution of zero-crossing crest heights represents a critical design input for a wide range of engineering applications. The present paper describes the development and validation of a new crest height model, suitable for application across a broad range of water depths. The purpose of this model is two-fold: first, to describe the amplifications of the largest crest heights arising due to nonlinear interactions beyond a second-order of wave steepness, and second, to incorporate the dissipative effects of wave breaking. Although these two effects act counter to each other, there is substantial evidence to suggest departures from existing models based upon weakly nonlinear second-order theory; the latter corresponding to current design practice. The proposed model has been developed on the basis of a significant collection of experimental results and a small subset of field measurements. It incorporates effects arising at different orders of nonlinearity as well as wave breaking in a compact formulation and covers a wide range of met-ocean conditions. Importantly, the new model has been independently validated against a very extensive database of experimental and field measurements. Taken together, these include effective water depths ranging from shallow water

Statistical distribution of free water surface over a mild bed slope for extreme wavefields

This paper examines the probability density function (PDF) of free water surface elevations in coastal areas. The functional form and properties of PDFs of extreme storms propagating over a mildly sloping bathymetry are investigated. This is facilitated through comparisons between experimental measurements and a wide range of probability models; the latter including both analytical and empirical distributions. The incident wave conditions correspond to realistic storm spectra (JONSWAP) and have been simulated as long random timeseries of 60-hour duration. The length of the records is sufficient to provide an accurate description of distribution tails. Six sea-states with varying offshore steepness have been generated and measured at different cross-shore locations. The cross-shore evolution of the wavefield initially leads to the development of nonlinear harmonics, both at low and high frequencies, and a broadening of the wave spectrum. This is enhanced by wave breaking particularly at shallower water depths or steeper sea-states. These result in rapid deviations from Gaussian theory with respect to the PDFs of surface elevations. Available models are generally successful in capturing nonlinear evolution arising at a second-order of wave steepness but cannot model the probability structure once a significant proportion of waves are breaking. In comparing the deviations between experimental data and model predictions, the best performing model is identified

A new wave height distribution for intermediate and shallow water depths

The present paper addresses the short-term distribution of zero-crossing wave heights in intermediate and shallow water depths. New physical insights are provided regarding the effects of nonlinearity, directionality, reduced effective water depth and finite spectral bandwidth. These are demonstrated through the analysis of a large database of experimental simulations of short-crested sea-states on flat bed bathymetries. A new wave height model is proposed building upon these physical insights and is calibrated using the experimental data. Independent comparisons between field measurements and the proposed model indicate that it is appropriate to a wide range of incident wave conditions and that it provides considerable improvement over existing models

An efficient method of defining the tail of a crest height distribution

The exceedance probability of wave crest elevation is a critical environmental input for the design/re-assessment of marine structures. With attention often focused on structural reliability, and in some cases survivability, the largest wave crests arising at the smallest exceedance probabilities, said to be located in the tail of a distribution, are of primary interest. This paper explains why present design practice may be non-conservative in the most extreme seas and outlines a new method by which the tail of the distribution can be defined using a relatively small number of deterministic wave events. This avoids the need to explore the entire distribution using very long (and expensive) random wave simulations. The new approach allows both an extension of the distribution to smaller exceedance probabilities and a concentration on the largest most design relevant crest heights. Having demonstrated the success of the proposed method by comparisons to laboratory data, the analysis is extended to include the effective prediction of the associated confidence intervals (CIs). With the highest waves subject to the largest statistical uncertainty, the paper explores the nonlinear changes in CI, demonstrates that these can also be accurately and efficiently defined, and explains how CI may be reduced. The focus of the paper lies in improved design calculations, based upon the nonlinear dynamics of extreme waves in realistic seas

On the average shape of the largest waves in finite water depths

This paper investigates the average shape of the largest waves arising in finite water depths. Specifically, the largest waves recorded in time-histories of the water surface elevation at a single point have been examined. These are compared to commonly applied theories in engineering and oceanographic practice. To achieve this both field observations and a new set of laboratory measurements are considered. The latter concern long random simulations of directionally spread sea-states generated using realistic JONSWAP frequency spectra. It is shown that approximations related to the linear theory of Quasi-Determinism (QD) cannot describe some key characteristics of the largest waves. While second-order corrections to the QD predictions provide an improvement, key effects arising in very steep or shallow water sea-states are not captured. While studies involving idealised wave groups have demonstrated significant changes arising as a result of higher-order nonlinear wave-wave interactions, these have not been observed in random sea-states.The present paper addresses this discrepancy by decomposing random wave measurements into separate populations of breaking and non-breaking waves. The characteristics of average wave shapes in the two populations are examined and their key differences discussed. These explain the mismatch between findings in earlier random and deterministic wave studies

Assessment of wave height distributions using an extensive field database

The present paper investigates the short-term statistical distribution of wave heights. Specifically, some of the most commonly applied wave height distributions are assessed using field measurements. The latter comprise of wave radar observations from 10 different locations in the North Sea and cover water depths between 7.7 m and 45 m. In total, the field database includes more than 200 million waves, making it one of the largest of its kind in this water depth regime. In using these data, the accuracy of existing wave height distributions has been examined and guidance is provided concerning the best performing models and their domain of applicability. Additionally, insights concerning the influence of key met-ocean parameters are also provided. Taken together, the results in this paper present an overview of the statistical behaviour of wave heights in finite water depths, as observed in the field

Laboratory investigation of crest height statistics in intermediate water depths

This paper concerns the statistical distribution of the crest heights associated with surface waves in intermediate water depths. The results of a new laboratory study are presented in which data generated in different experimental facilities are used to establish departures from commonly applied statistical distributions. Specifically, the effects of varying sea-state steepness, effective water depth and directional spread are investigated. Following an extensive validation of the experimental data, including direct comparisons to available field data, it is shown that the nonlinear amplification of crest heights above second-order theory observed in steep deep water sea states is equally appropriate to intermediate water depths. These nonlinear amplifications increase with the sea-state steepness and reduce with the directional spread. While the latter effect is undoubtedly important, the present data confirm that significant amplifications above second order (5–10%) are observed for realistic directional spreads. This is consistent with available field data. With further increases in the sea-state steepness, the dissipative effects of wave breaking act to reduce these nonlinear amplifications. While the competing mechanisms of nonlinear amplification and wave breaking are relevant to a full range of water depths, the relative importance of wave breaking increases as the effective water depth reduces

Adaptive design of coastal flooding defences: a coupled experimental and numerical approach

This paper presents a new set of physical model tests on wave propagation over complex coastal bathymetry and wave overtopping. These relate to a coastal defence with a steep front wall and a setback wall. The experimental measurements are reproduced numerically using the SWASH model. Experimental measurements are also compared to state-of-the-art numerical and analytical methods of predicting wave overtopping (Artificial Neural Networks, EurOtop equations). Considerable discrepancies between experiments and predictions are observed. These are resolved using a newly proposed method, which adapts theoretical predictions to measurements. Finally, this method is verified against additional experimental data and is shown to provide an effective way to define adaptations to existing infrastructure to satisfy engineering design criteria