Journal of Waterway, Port, Coastal, and Ocean Engineering

The solution to the problem of the interaction of linear waves with a composite breakwater is presented and is applied to determine wave reflection and transmission as well as wave loads on a caisson founded on a multilayered rubble base. The results show that the bench width has little effect, whereas the rubble base height has a significant effect on wave reflection and transmission and on wave loads on the caisson. The results also show that complex, thick, or less permeable armor layers increase the effect of rubble base. Moreover, the results show that the rubble damping properties should be included in the analysis of wave reflection and transmission, and wave loads on a caisson, and that the damping can be described satisfactorily by the Darcy damping law. The present method can be applied in a straightforward manner to an excitation provided by wind waves and, before a more advanced approach is attempted, some cases associated with nonlinear wave excitation may partially be analyzed with a modification to the present approach. Theoretical results are in fairly good agreement with experimental data.

Shoaling and breaking of solitary waves is computed on slopes from 1:100 to 1:8 using an experimentally validated fully nonlinear wave model based on potential flow equations. Characteristics of waves are computed at and beyond the breaking point, and geometric self-similarities of breakers are discussed as a function of wave height and bottom slope. No wave breaks for slopes steeper than 12°. A breaking criterion is derived for milder slopes, based on values of a nondimensional slope parameter S_o. This criterion predicts both whether waves will break or not and which type of breaking will occur (spilling, plunging, or surging). Empirical expressions for the breaking index and for the depth and celerity at breaking are derived based on computations. All results agree well with laboratory experiments. The nonlinear shallow water equations fail to predict these results with sufficient accuracy at the breaking point. Prebreaking shoaling rates follow a more complex path than previously realized. Postbreaking behaviors exhibit a rapid (nondissipative) decay, also observed in experiments, associated with a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

A model and estimation procedure are proposed for the recurrence rate of hurricanes in the Gulf of Mexico. The model and the estimation procedure are based on the representation of the hurricane tracks as a locally linear line process. The spatial variation of the intensity of the process is estimated through a kernel estimation procedure. The optimal degree of smoothness is selected through a resampling procedure and goodness-of-fit statistics. Simulations demonstrate that the model and estimation procedures can detect statistically significant spatial variations in the rate of occurrence of hurricanes. The emphasis of the study is on storms that have affected the offshore areas between the northwest Florida panhandle and the Texas coast. The optimal model indicates that the spatial variation of the recurrence rate is statistically significant and that the highest frequency of hurricanes occurs offshore west of New Orleans. The implications from a hurricane hazard point of view are most significant for deepwater offshore projects, while the recurrence rate appears to be almost constant along the western coast of the Gulf in shallower waters.

Observational and theoretical evidence suggests hurricane severity can be affected by local oceanographic features. The most important of these features in the Gulf of Mexico are the Loop current and its associated eddies. These features are large bodies of warm subsurface water that, theory suggests, can act as an energy source for passing hurricanes. Present design standards for the offshore oil industry assume no spatial variability, so these findings have substantial financial implications for design of new structures and requalification of thousands of existing ones. We propose a statistical model and an estimation procedure that accounts for the spatial variation of the probability distribution function of hurricane severity. The model is based on the representation of the hurricane process as a marked line process where the hurricane tracks are idealized as linear segments with respect to a given location, and where the marks measure the severity of hurricanes. The efficiency of the estimation procedure is evaluated through simulations for different types of spatially dependent probability distribution functions. The procedure is finally applied to a data set comprising the 100 most severe hurricanes in the Gulf of Mexico from 1900 to 1989.

We investigate the parameterization of the vertical structure of horizontal velocity in a family of weakly nonlinear, weakly dispersive (Boussinesq) models developed by Nwogu. That model contains a free parameter that specifies the depth about which the assumed quadratic velocity profiles are expanded, with most standard formulations recovered by particular choices of this free parameter. Nwogu chose to optimize this model by selecting the parameter to best fit the linear dispersion relation. Here we test the model by applying it to the nonlinear case of shoaling of regular (cnoidal) waves. A new data set documenting the vertical dependence of horizontal velocity is presented and is used to evaluate the range of values of the free parameter for which the model gives good results. We show that the Boussinesq model optimized for the best linear dispersion relation also gives the best approximation to the local vertical structure in this strongly nonlinear case.

The exact solitary wave solution to the Boussinesq equations, which was given in an implicit integral form, is further studied in the present note. Through numerical curve fitting, an explicit closed-form empirical solution whose profile is nearly identical to the exact solution is obtained. Discussion and comparison between solitary wave solutions based on the Boussinesq model and higher-order theories of the Euler equation are presented.