Journal of Waterway, Port, Coastal, and Ocean Engineering

The design of bottom‐laid deep‐ocean pipelines requires estimates of the dynamic stresses and motions that result from a random wave environment. A 3‐D finite element algorithm is presented that estimates the large displacements of pipelines sliding on irregularly contoured marine sediments and subjected to episodic hydrodynamic loads. Nonlinear elastic‐plastic springs simulate transverse and axial bottom resistances for both cohesionless and cohesive sediments. Inclusion of a hydrostatic pressure differential across the pipe wall modifies axial stresses and influences the flexural stiffness of the finite element model through the geometric stiffness matrix. Hydrodynamic inertia and nonlinear viscous drag forces are represented by a relative‐motion form of the Morison equation. The equations of motion during each episode of extreme wave activity are integrated using the Newmark method of implicit integration. Within each time step, a Newton‐Raphson scheme of iteration is used to satisfy equilibrium while accurately predicting the nonlinear path‐dependent response. An updated Lagrangian formulation shifts the reference configuration of the pipeline and separates rigid‐body movements from pipeline deformations. This provides a large‐deflection, small‐strain, transient analysis of the pipeline motion, which is capable of computing finite‐amplitude motions that have been accumulated over the random wave episodes.

A Strategic Petroleum Reserve is being created along the Gulf coast of southeast Texas and southern Louisiana. Storage caverns have been created in salt domes using a leaching process, and the resultant brine solution is pumped offshore through a submerged pipeline where it is discharged through a multiport diffuser. The storage caverns are subsequently filled with oil to form the reserve. The vertical extent (height) and the dilution of the brine at the Strategic Petroleum Reserve's Bryan Mound diffuser site located offshore of Freeport, TX, are measured by acoustic methods and a conductivity, temperature, and depth sensor. The field data were analyzed using linear regression techniques, and new empirical equations were obtained to predict the vertical extent and dilution. The equation for the vertical extent of the brine jets predicts greater heights than those obtained from similar equations based upon laboratory studies. The dilution data of the dense jet results in an empirical equation that agrees well with the laboratory results but predicts higher values than previous offshore measurements at the same diffuser.

The development of the turbulent boundary layer around a circular cylinder in oscillatory flow is investigated by the depth integrated equation of momentum. The shape of the velocity profile is assumed to be log‐linear. The development of the downstream separation point with time is studied as a function of the Keulegan‐Carpenter number and relative roughness for a rough cylinder, and as a function of the Reynolds number for a smooth cylinder. The paper suggests the parametric variation in the drag coefficient with the Reynolds number or relative roughness at small KC‐numbers (smaller than about 8–10) where vortex shedding does not take place.

Details of a numerical model study to predict the tidal circulation observed and measured in the lee of Rattray Island, Australia are presented. The hydrodynamic model is of the two‐dimensional depth integrated type, with particular emphasis being placed on the modeling of the advective accelerations and the lateral mixing in the free shear layer in the island's wake. The component of free shear layer turbulence includes a constant eddy viscosity approach in the mixing zone and the use of a semi‐empirical lateral velocity distribution. The numerically predicted circulatory velocity fields have been compared with field measurements, taken at 26 sites, aerial observations and Landsat imagery. The comparisons between both predicted and measured results are encouraging, with the eddy dimensions and circulation strength being similar for all tidal phases. Various other simulations are described, which chiefly suggest that, for this study: (1) The eddy characteristics are reduced when the lateral shear stress is neglected; (2) no eddy is reproduced when the advective accelerations are excluded; (3) bathymetric effects are significant; and (4) geostrophic effects are important at water elevation boundaries.

In the design and development of ports, cost‐benefit analyses are often used to select the final design. These analyses show on the one hand the costs, i.e., capital and maintenance costs for dredging and investment costs, and on the other hand the benefits of a larger transport volume. The economy of a port is substantially influenced by the dimensions of approach channels and port entrances. To determine optimal dimensions of a harbor, the vessels that will call at the port have to be considered, because the channel and port dimensions are largely influenced by the behavior of the vessels. In the prediction of ship motions, simulation techniques have proven to be adequate tools. Two such simulation techniques are discussed: one related to horizontal ship motions; the other related to vertical ship motions.

Because a gravity structure is placed on the ocean floor it is important to investigate the effect of the water pressure on the bottom of the pads of the structure. Any communication between the underneath of the structure and outside will introduce pressure through scouring or porous foundation which will alter the vertical force and overturning moment on the structure due to waves. The effect of the bottom pressure on these quantities is investigated in a test with a gravity drilling platform model in which both pressures and forces were measured. It is shown from experimental and computed results that while the bottom pressure will substantially alter the vertical force, its effect on the overturning moment is also significant. Moreover, for a structure resting on pads with a small gap between the pads and the floor it is found that the bottom pressure can be estimated from the pressure outside the pads with reasonable accuracy.

Recent experimental studies show that the impact pressures resulting from a wave breaking directly on a vertical wall are very severe in magnitude and short in duration. Some evidence in the literature suggests that these kinds of pressures are capable of causing structural damage to composite‐type breakwaters. This study is mainly concerned with the theoretical analysis of the response characteristics of a caisson plate under the wave impact loading. Impact pressure data is taken from recent experimental work. In the dynamic analysis of the caisson plate the classical elastic plate theory is used and the numerical results for the dynamic values of moments and transverse displacement are obtained by employing the method of finite elements together with a mode superposition technique. A new criterion is proposed to determine the number of modes to be considered in the analysis. The time histories of the moments and transverse displacement exhibit similar patterns and the dynamic values are considerably greater than the static values. The latter values are obtained by representing the maximum impact pressure distribution as a static load. A procedure for the dynamic design of caisson plates is proposed which is based on the dynamic magnification factor.

Mathematical simulation models are of growing importance in the design stage and for the operation of mooring facilities at exposed locations. In this paper such a model is described for the prediction of motions and mooring loads of ships and other floating structures moored in irregular waves, wind, and current. The mathematical model is based on the equations of motion in the time domain. This approach allow nonlinear and asymmetric mooring loads and arbitrarily in time varying excitation of the vessel. Input variables are: environmental conditions; mooring layout; elasticity characteristics of mooring lines and fenders; and geometry of the vessel. Output information includes: time histories; spectra and statistical values of motions, and mooring loads. Results are presented of an extensive validation study on the behavior of a 200,000 TDW tanker moored to an offshore jetty in shallow water. From the results it may be concluded that there is good qualitative and quantitative agreement between the results of the computer model and the experimental results.

The interaction of small amplitude water waves with a patch of bottom ripples is studied using the Boundary Integral Equation Method (BIEM). Normal and oblique wave incidence is examined for reflection coefficients and the laboratory data of Davies and Heathershaw are compared to the numerical results, with the conclusion that the analytical model of Davies and Heathershaw overestimates the reflection coefficient at resonance. Comparison of BIEM results for oblique incidence is made with an extension of the recent work of Mei showing good agreement, even for large amplitude ripples.

The wave motion in the vertical planes containing the loci of free surface elevation peaks in a periodic short‐crested wave, synthesized as the sum of two component waves, is exactly two‐dimensional. It is shown that the linear and nonlinear theories that have been developed for long‐crested twodimensional waves are valid for the wave motion of short‐crested waves in the previously defined planes, provided that the wave height, $H_c\text{,}$ defines the total vertical difference between peak and depression (instead of crest to trough as in the case of long‐crested waves) and the wave length $L_c$ is the distance between peaks. It is also shown that the Stokes theory for limit waves is valid for short‐crested waves and that the breaking criteria that are based on the Stokes theory are also applicable to short‐crested waves, with a correction that is a function of the angle between the crests of the two primary wave components. The maximum possible free surface elevation of the peak of shortcrested waves is then obtained for engineering applications.

The Stream Function Wave Theory has been shown to produce waves with multiple crests. This paper shows that the multiple-crested waves are not real, but an attempt by the numerical theory to represent a periodic wave train of shorter period. A procedure to restrict the solution technique to only single-crested waves is provided.

A statistical analysis is performed to determine the probability distribution applicable to spectral integrals. This analysis shows that, since the spectrum of a stationary Gaussian random process follows a chi-square distribution, the integral of the spectrum will also be chi-squared. The number of degrees of freedom of the spectral integral depends on the shape of the spectrum. As a practical example, confidence limits are calculated for significant wave height estimates obtained by integrating the wave spectrum.