Parameterization of Wave Breaking Probability and Whitecap Coverage

The model for whitecap coverage and wave breaking probability are parameterized by the dimensionless wind fetch X^-. This paper aims at replacing X^- with other parameters such as the average wave period T^-, wind speed U10 or wave age ξ in order to improve the suitability and convenience of the model for application. First, W and B are expressed in terms of T^- and U10, which are relatively easy to measure in the field. Further, U10 is replaced with the friction velocity U. by use of the empirical relationship. As wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, W and B are then expressed as a simple function of wave age, respectively. The new forms of the model obtained are W= 1 - Ф（3.02ξ0＂76） and B = exp（ - 4.54ξ^1.52） . The two forms are mere applicable in pracrice, since ξ is relatively easy to measure or determine from wave and wind records. Comparisons between these expressions and data collected from published literature are made and agreement is fairly good.

Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact renders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabilistic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks if the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4. Then the JONSWAP spectrum is used to represent the fetch limited sea waves in deep water, so as to relate the probability of wave breaking and the whitecap coverage with wind parameters. To this end, the time averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.

Risk Analysis of Breakwater Caisson Under Wave Attack Using Load Surface Approximation

A new load surface based approach to the reliability analysis of caisson-type breakwater is proposed. Uncertainties of the horizontal and vertical wave loads acting on breakwater are considered by using the so-called load surfaces, which can be estimated as functions of wave height, water level, and so on. Then, the first-order reliability method（FORM） can be applied to determine the probability of failure under the wave action. In this way, the reliability analysis of breakwaters with uncertainties both in wave height and in water level is possible. Moreover, the uncertainty in wave breaking can be taken into account by considering a random variable for wave height ratio which relates the significant wave height to the maximum wave height. The proposed approach is applied numerically to the reliability analysis of caisson breakwater under wave attack that may undergo partial or full wave breaking.