Scour around pipelines, piles and sea walls

Review of knowledge regarding scour near pipelines and other offshore structures

Mathematical Model to Predict the Behavior of Deep-Draft Vessels in Restricted Waterways

Presently deep-draft navigation channel analysis, design and review is based on empirically derived ratios of the design vessel's dimensions. Because of radical changes in vessel operation purposes and characteristics, these ratios can no longer be safely or economically applied. The mathematical model and related theory described in this document provide the engineer with a comprehensive tool in the design and review of deep-draft navigation channels. Through its use he will be able to predict values of squat, bank suction forces and moments, equilibrium drift and rudder angles, and heights of ship-generated waves for varied channel configurations, ship positions and ship velocities. Through the determination of channel section configuration sensitivity, an optimal design both operationally and economically can be achieved

Effect of Wave-Current Interaction on the Wave Parameter

The interaction of a gravity wave with a steady uniform current is discussed in this paper. Analysis indicates there is no dominant difference in the results obtained when employing either the equation of conservation of wave energy flux or the equation of conservation of wave action flux. Numerical calculations of the wave length change by different non-linear wave theories show that errors in the results computed by the linear wave theory are less than 10 percent within the range of 0.15 <= d/Ls <= 0.40, 0.01 <= Hs/Ls <= 0.07 and -0.15 <= U/Cs <= 0.30, where d = water depth, Hs = wave height in still water, Ls = wave length in still water, Cs = wave celerity in still water, and U = surface current velocity. Numerical calculations of wave height change employing different wave theories show that errors in the results obtained by the linear wave theory in comparison with the non-linear theories are greater when the opposing relative current and wave steepness become larger. However, within range of the following currents such errors will not be significant. These results were verified by model tests. Nomograms for the modification of wave length and height by the linear wave theory and Stokes' third order theory are presented for a wide range of d/Ls, Hs/Ls and U/Cs. These nomograms provide the design engineer with a practical guide for estimating wave lengths and heights affected by currents.Ocean Engineering Progra

Nonparametric and Parametric Estimation of Wave Statistics and Spectra

A nonparametric bivariate density estimation technique is developed employing tensor product B-splines to provide a concise wave data summary. Most of the existing nonparametric techniques involve a certain level of subjectivity in the choice of smoothing parameters. A criterion based on the least squares concept is proposed to remove the subjective choice of smoothing parameters. Numerical experiments, in which random variables are generated from a known bivariate independent normal distribution and the modified Longuet-Higgins distribution, show that the technique reproduces the population density functions well. However, due to Lack of the shape preserving property of B-splines, the positivity of the density function cannot be guaranteed. An alternative spectral estimation procedure is proposed, extending the idea of Bretschneider (1959). The alternative spectrum is the second moment of the wave height of the joint probability density function (pdf) in terms of the frequency domain, and is named the PDF spectra. Comparison of the latter with other spectral estimators such as the FFT spectral window estimator and the autoregressive spectral estimator shows good agreement. The nonparametric joint pdf provides a concise representation of longterm wave data from which one can obtain not only the usual wave statistics, but the wave spectra as well. That is, the wave spectrum is simply a subset statistical function contained in the bivariate pdf for wave height and period

Effects of Slope Roughness on Wave Run-up on Composite Slopes

A comprehensive study of the wave run-up phenomena on single and composite slopes was conducted in order to determine the effects of slope roughness on regular and irregular wave run-up on composite sections, to determine the effects of slope roughness on the velocity distribution in the uprush zone, to investigate the energy loss in the uprush zone due to turbulence and bot tom dissipation and to compare regular and irregular wave run-up on roughened slopes with wave runup on smooth slopes. Monochromatic wave tests were run using wave periods of 1.00 sec, 1.56 sec and 1.86 sec in water depths of 1.2 ft, 1.5 ft and 1.8 ft. Equivalent deep water wave heights were varied from 0.113 ft to 0.443 ft while the mean wave energy densities (E ) were varied from 0.0006 ft^2/sec^-1 to 0.0165 ft^2/sec^-1. Wind (irregular) wave tests were run in water depths of 1.2 ft, 1.5 ft and 1.8 ft. Wave periods varied from 0.72 sec to 0.83 sec, while equivalent deep water wave heights varied from 0.290 ft to 0.396 ft and the mean wave energy densities varied from 0.0100 ft^2/sec^-1 to 0.0228 ft^2/sec^-1. Three model structures [single (1 on 1-1/2 slope, composite 1 on 1-1/2 slope with 1.5 ft berm) section and composite (1 on 1-1/2 slopes with 3.0 ft berm) section] were studied in a wind, water-wave flume. Three roughness conditions (smooth, parallel strips, and a symmetric block pattern) were investigated. The following conclusions were drawn from the study: 1. The water depth affected the relative wave run-up (R) of the Long waves. 2. The reflecting capability (power) of the single (1 on 1-1/2 slope) was not significantly affected by the slope roughness. 3. The reflect!ng capability (power) of the composite (1 on 1-1/2 slopes with berm) section was not significantly affected by the slope roughness. 4. The elevation of the berm with respect to the still water level had a significant effect on the reflecting capability (power) of the composite (1 on 1-1/2 slopes with berm) section. 5. The maximum reduction of wave run-up occurred with the water depth equal to the berm elevation. 6. The parallel strip roughness element was the most efficient dissipator of the wave run-up energy on the composite (1 on 1-1/2 slopes with berm) section. 7. The wave uprush velocity on the smooth (1 on 1-1/2) slope was approximately seven-tenths of the wave celerity. 8. The slope roughness reduced the maximum relative uprush velocity on the 1 on 1-1/2 slope. 9. Due to the changing mean velocity in the uprush zone the level of turbulence could not be measured. 10. No significant difference between monochromatic wave run-up and wind wave run-up was noted on either the single (1 on 1-1/2) slope or the composite (1 on 1-1/2 slopes with berm) section. A new method of determining wave run-up using the mean wave energy density is proposed.Sea Grant Progra

Estimation and Analysis of Horizontal Bottom Velocities Due to Waves

Maximum bottom velocities caused by waves were calculated using digital computers. Four wave theories, Airy, Stokes third order, Cnoidal and Solitary,were applied in the computation. Results of the study were tabulated and presented graphically to highlight the importance of various parameters affecting the maximum bottom velocity. It is suggested that maximum bottom velocities under a wave crest be considered while estimating the sediment movement and designing offshore pipelines, platforms, and underwater objects.Ocean Engineering Progra

Sediment Movement Induced by Ships in Restricted Waterways

A numerical model using the momentum theory of the propeller and Shields' diagram was developed to study sediment movement induced by a ship's propeller in a restricted waterway. The velocity distribution downstream of the propeller was simulated by the Gaussian normal distribution function. The shear velocity and shear stress were obtained using Sternberg's formulas. Once the ship's speed, depth of the waterway, RPM and diameter of the propeller, and draft of the ship are given, the velocity distribution and the grain size of the initial motion could be obtained from this model. A computer program was developed to solve it. Case studies are presented to show the influence of significant factors on sediment movement at the channel bottom induced by a ship's propeller.Ocean Engineering Progra

Wave Forces on Models of Submerged Offshore Structures

The results of a model study of the farces caused by oscillatory waves on large rectangular tank-like submerged objects are presented. Three phases of the problem were examined: 1) description of the forces in terms of dimensionless parameters, 2) description of the effect of large wave heights which are of importance to the designer, and 3) the presentation of a format to be used in model studies on submerged structures. Theoretical studies of the problem have assumed wave heights to be small and the forces to be entirely inertial. However, of interest to the engineer are the forces caused by the larger waves generated by severe storms. In the model study the forces caused by the larger waves were determined and the effect of the water particle velocity in producing a drag force was examined. The relationships between the fluid particle displacement and the coefficients of mass and drag were evaluated. Previous studies indicate that particle displacement is related to the values of empirical coefficients assumed by previous investigation. The experimental results are given in a dimensionless form. Provided the laws of modeling are followed, and there are no scale effects, these results may be used to determine the forces on prototype structures in the ocean

Scour of flat sand beaches due to wave action in front of sea walls

The erosion of sand beaches due to oscillatory water particle motion of non-breaking waves can be of importance, particularly where such a beach is fronted by a sea wall supported on spread foundation. Laboratory study was conducted with natural beach sand; waves were generated mechanically. Geometric variables included the inclination of sea walls front 15 to 90 degrees from the horizontal and dynamic variables included ratio of ''lave length to water depth and wave height to water depth. It has been determined that the "ultimate" depth of scour is a function of wave height and that the location of scour is a linear function of wave length