Journal of Waterway, Port, Coastal, and Ocean Engineering

This paper presents the results of an experimental investigation on scour below pipelines exposed to waves. The effect of lee‐wake of the pipe is the key element in the scour process, and it is demonstrated that the Keulegan‐Carpenter number is the main parameter that governs the equilibrium scour depth. Based on the presently available data, a design equation is established, relating the equilibrium scour depth to the Keulegan‐Carpenter number for the live‐bed situation and for a pipe in contact with the bed. The latter equation indicates that the equilibrium scour depth normalized with the pipe diameter is proportional to the square root of the Keulegan‐Carpenter number, the proportionality constant being 0.1. The effect of Shields parameter on the final scour depth is found to be quite weak. It is also found that the surface roughness of the pipe imposes practically no influence on the scour process. The pipe position with respect to the bed appears to be an important parameter in determining the equilibrium scour depth.

While studying the bathymetric transformation of ocean waves propagating into a coastal region, the engineer often invokes the concept of the significant wave to represent the offshore irregular sea state. As an approximation, the propagation characteristics of a regular wave train (with properties equal to that of the significant wave) are determined, instead of those of the actual irregular sea state. However, recent experimental investigations by Vincent and Briggs have shown that for the case of combined refraction‐diffraction of waves by a shoal, the propagation characteristics of the irregular and equivalent regular (monochromatic) wave conditions can be vastly different. At the same time, researchers are investing substantial effort in the construction of accurate numerical refraction‐diffraction models for monochromatic waves. Although the monochromatic representation gives a poor approximation of the spectral conditions, this study shows that a monochromatic refraction‐diffraction model can be used to make spectral calculations that agree closely with the actual irregular conditions observed in a hydraulic model. Further, these calculations can also help explain all the observed differences in the propagation of regular and various types of spectral conditions over the shoal.

A simple theoretical model was applied to interpret the characteristics of an estuarine front that forms at the early stage of each flood tide off Newport News Point, in the lower James River, Virginia. The observed depths of diving of denser water at the front, and the upriver movement of the front are explained theoretically. The construction of a man‐made island to facilitate port expansion was proposed for downriver of the front. Its effect on the flood current approaching the front is quantified with a vertically averaged two‐dimensional numerical model. The theory is used to predict the impact of the proposed island on the frontal characteristics, particularly with respect to the entrainment and transport of oyster larvae to the lower portion of the water column, where net transport is upriver toward seed‐oyster beds. Applications of the front theory, results of the numerical model, and oyster‐larvae studies indicate that the transport capacity of the front would be markedly reduced by island construction at the proposed sites.

The simple case of sand accretion behind an impermeable breakwater parallel to the shoreline with normally incident waves is treated. The cuspate foreland or salient so formed has an apex whose location from the breakwater is dependent upon the ratio of the length of the breakwater to its distance offshore. The waterline shape on each side of the apex can be defined by relationships from crenulate‐shaped bays formed between headlands. Since static equilibrium is assumed these shapes are independent of wave characteristics, sedimentary material used in models, and location of the original breaker line. The intersection of the two adjacent beaches at the centerline as the distance from the breakwater can be used in identifying limits for tombolo formation.

Properties of surface‐elevation spectra representative of nonlinear deep‐water wind waves are examined theoretically. For a wave field characterized by second‐order nonlinearities, expressions describing the spatial covariance and the directional wave‐number spectrum of the surface geometry are derived. The nature of these quantities are then examined with emphasis on the high‐wave‐number attenuation of spectral amplitudes. It is found that, if the spectrum of the firstorder linear wave field decays as $k^{-p}$ toward the high‐wave‐number extreme, then the spectrum of the nonlinear wave field must decay as $K^{-p+2}\text{.}$ This condition coupled with the saturation/equilibrium range concepts is shown to necessitate the existence of certain upper‐limit asymptotes to the high‐frequency attenuation of linear‐wave spectra. Practical implications of this result are explored with reference to low‐pass filtering of wave records, and the representation of Gaussian sea waves based on various empirical and/or theoretical forms of wind‐wave spectra.

An experimental program in which entrainment and movement of air bubbles within the voids of rubble‐mound breakwater models were investigated is described. Aeration was evaluated as a function of type of armor unit (stones, spheres, and cubes), breakwater slope, relative geometry of the structure, and type of core material. Aeration resulting from both external wave breaking and flow separation was observed. The relative extent of aeration was a function of the type of breaking wave observed. Aeration was more severe in structures constructed with highly permeable cores. Variations in void geometry and orientation had a significant influence on the motion of air bubbles into the structure.