Journal of Waterway, Port, Coastal, and Ocean Engineering

This paper discusses some of the existing statistical models for the analysis of extreme value data in the case of independence, pointing out their excellence and possible sources of error. Initially, the concept of order statistics is introduced, and the joint distribution of any set of order statistics is given. As simple examples, the distribution of the maximum, the minimum, any single order statistic, or any pair of order statistics are derived. Then, the problem of limit distribution is raised and carefully analyzed making a clear distinction between maxima and minima. It is shown that all models can be grouped in the Von Mises‐Jenkinson families, which include the three classical families. Several methods for selecting an adequate limit distribution based on data, including probability papers, least‐squares methods, and the curvature method are described. To clarify concepts, several illustrative examples of applications are included. Finally, a practical method for determining the limit distribution is described in detail.

Results of recent research on experimental investigation of wave‐fluid particle kinematics just prior to breaking using laser Doppler anemometry are presented. Extreme transient waves, similar to those found in hurricane Camille, and an “equivalent” regular wave, often used for design purposes, are generated and their kinematics measured. The kinematics of transient waves of smaller height are also measured to evaluate the effect of wave height, and these data are compared to Stokes third‐order theory. Due to particular asymmetries not present in the large regular symmetric wave, the transient wave kinematics under the crest are shown to be much more severe above the still water level and somewhat less severe below. The stretching method used for the simulated transient wave underestimates the horizontal velocities in the crest and overestimates them below the still water level. These comparisons suggest that it would be worthwhile to further investigate the use of extreme waves as more realistic design waves and to develop a wave theory that accounts for the effect of the asymmetries.

In coastal rivers, the water level is greatly affected by the upstream movement of a tidal wave. The latter creates higher flood stages that enlarge the flood plain areas and increase potential damages. In such rivers, the water level is not solely a function of the flow discharge but rather a joint function of both the discharge and tidal phenomena. The interference of the tidal backwater with the normal flow of the river causes a disruption in the normal stage‐discharge relationship. This paper attempts at formulating a linear relation between tidal water level and river flow discharge that can be used for the predictions of water level in coastal rivers and estuaries. Numerical applications were performed on the St. John river (New Brunswick) and the St. Lawrence river (Québec) in Canada with satisfactory results.

A linear theory equation is presented for estimating water velocity parameters beneath reflected, two‐dimensional, irregular, nonbreaking waves as a function of the incident wave spectrum, water depth, and spatial location. The estimation procedure requires specification of wave reflection and phase shift as a function of frequency. For the special case of normally incident, unidirectional, nonbreaking irregular waves being perfectly reflected by a vertical wall, the equation provides estimates of near‐bottom (above boundary layer) fluid particle velocity parameters as a function of only the incident wave spectrum, water depth, and distance from the wall. Comparisons between laboratory fluid velocity measurements and velocity estimates based on the measured incident spectrum are good for this special case. Furthermore, the distribution of peak horizontal velocities compares well with estimates based on the Rayleigh distribution. For two cases of a TMA spectrum wherein the significant height and peak period vary but other shape parameters are held constant, explicit formulas are given to estimate maximum bottom velocity parameters as a function of water depth, peak period, and significant height.

Using the results of large‐scale wave tank tests of monochromatic waves breaking on sandy beaches, Larson and Kraus have shown that storm (barred) and normal (nonbarred) equilibrium beach profiles can be segregated in terms of two‐dimensionless parameters, which involve wave and sediment characteristics. Here, by rearranging their results, a single dimensionless parameter is developed that predicts the occurrence of storm or normal profiles. The profile parameter $(P=g{H}_0^2/(w^{3}T\left)\right)$ uses deep‐water wave characteristics to distinguish the two profile types. Using shallow‐water data the shallow‐water Dean number, $H_b/\left(\mathrm{wT}\right)$ can serve the same purpose. Further, a Froude number representation of the sediment fall velocity, $w^2/\left({\mathrm{gH}}_0\right)\text{,}$ is shown to be an important parameter for equilibrium profiles.

The wave-induced vertical effective stress near seabed surface is approximately expressed by subtracting the pore-water pressure from the sum of the vertical static effective stress in calm water and the wave pressure acting on the seabed. Among many parameters, a ratio of the shear modulus of the solid skeleton to the effective bulk modulus of the pore-water is an important parameter to dominate the vertical effective stress and the resultant momentary liquefaction at wave trough phase. Another important parameter is a nondimensional quantity proportional to a product of the permeability coefficient and the shear modulus. As the former parameter becomes large and the latter one becomes small, a possibility that the vertical effective stress in the solid skeleton becomes zero at the wave trough phase increases. The maximum depth of being zero vertical effective stress, that is, the depth of liquefaction, is about half the wave height.

Armor stability on submerged conventional breakwaters is examined using a hybrid method based on experimental, numerical, and empirical results. Four test runs are conducted to measure the horizontal fluid velocities and free-surface elevations over a submerged breakwater caused by a solitary wave. These measurements are used to evaluate the numerical model called IBREAK. The agreement between the measured and computed results is found to be fair except that IBREAK overestimates the velocities immediately landward of the crest of the submerged breakwater for the case of small submergence. The comparison also shows that the horizontal velocity over the breakwater decreases with the increase of its submergence. The reduction of the horizontal velocity is then related to the increase of armor stability on the breakwater with the increase of its submergence. The present method predicts the significant increase of the armor stability resulting from the moderate reduction of the maximum horizontal velocity with the increase of the submergence depth. Comprehensive data are required to verify the predicted armor stability.

A new formula for the stone weight in the breakwater armor layers is proposed. It is obtained as a result of the statistical analysis of 21 of the existing expressions for the stone weight. The statistical approach is proved to be applicable. Various statistical procedures were employed in the analysis. The derived formula is a statistical generalization of the formulas considered. It holds for the wide range of the relevant parameters.

The limit of run-up on beaches has important coastal engineering and management implications. However, existing guidance on estimating run-up on sandy beaches is sparse and is based on parameters and models developed for run-up on structures. In particular, run-up is often scaled with Hunt's equation, also called the Iribarren number or the surf parameter. It is shown that one term of that parameter, the beach-slope term, can be omitted from engineering models of extreme values of run-up on beaches. Philosophically, the beach slope is a dependent variable on sandy beaches that are free to respond to the incident wave energy and thus should not be included in a run-up model. Practically, the beach slope is hard to estimate a priori for the engineer. Holman's data on extreme run-up levels during a wide range of wave conditions at Duck, North Carolina are used to show that removing beach slope does not cause any reduction in run-up model ability.