Showing papers in "Journal of Waterway Port Coastal and Ocean Engineering-asce in 1990"

Scour Below Pipelines in Waves

Abstract: This paper presents the results of an experimental investigation on scour below pipelines exposed to waves. The effect of leewake of the pipe is the key element in the scour process, and it is demo...

Distribution of Large Wave Heights

Abstract: The statistical distribution of zero-crossing wave heights is considered within the context of a previous theory proposed by the writer some years ago. The underlying model, definitions, and assumptions are reexamined systematically to develop asymptotic approximations to the probability density, exceedance probability, and statistical moments of wave heights larger than the mean wave height. The asymptotic results have closed forms, and thus are easier to use in practical applications than the original theory, which requires numerical integration. Comparisons to empirical data are given to show that the present asymptotic theory produces the observed statistics of large wave heights faithfully to within 1%. Further, comparisons with other relevant theories also reveal that if one remains true to the theoretical definitions, then the present theory is the most accurate in predicting the exceedance distribution of large wave heights. Finally, the asymptotic theory is coupled with the statistics of wave periods to derive a theoretical expression for the joint distribution of large wave heights and associated periods. The predictive utility of this last result remains to be explored.

Wave diffraction through offshore breakwaters

Abstract: The interaction of water waves with a long linear array of offshore breakwaters is examined to determine the reflection and transmission coefficients for these structures, providing data on the sheltering afforded by these structures. Two variational methods and an eigenfunction expansion method are used to determine the reflection coefficients for waves with wavelengths longer than the distance from gap to gap in the breakwater array. The eigenfunction method is also used for breakwaters, where the spacing between the gaps is longer than the water wavelength. For this case, analogous to scattering of light by a grating, numerous monochromatic directional wave trains can be generated in the region behind (and in front of) these breakwaters, which can lead to the generation of rip currents, beach cusps, and other periodic phenomena on beaches behind the structures.

Soft mud response to water waves

Abstract: Motion within soft mud beds, wave‐induced bed shear stress, and wave attenuation under small amplitude waves are briefly examined using an analytic approach to gain insight into the mechanism by which coastal mud responds to water waves. The cohesive mud bed is discretized into layers of simple linear viscoelastic material characterized by constant density, viscosity, and shear modulus of elasticity, for approximately simulating depth‐varying bed properties as well as energy dissipation. Model results on wave orbital velocities, dynamic pressure, and wave attenuation are compared with limited data from wave flume tests on partially consolidated beds under relatively low deformations and show acceptable agreement. Wave attenuation coefficients exhibit dual dependence on the degree of bed consolidation and sediment composition. In the absence of adequate data on bed shear stress over mobile, partially consolidated mud beds, this method offers an approximate procedure useful for bed shear stress estimation r...

Generation of long waves in laboratory

Abstract: A consistent theory is presented for generating arbitrary, finite‐amplitude, long waves at any location in a two‐dimensional, constant‐depth wave tank using a vertical paddle‐type wavemaker. The theory consists of solving an inverse evolution problem of the Korteweg‐de Vries equation; given specific initial data the boundary motion that produces that data is determined. The theory also suggests the appropriate method for calculating the force on the wavemaker. Application of this theory allows for the laboratory generation of very detailed single waveforms at arbitrary lengths away from the wave‐maker; this formalism obliterates the limitations of the existing shallow‐water wavemaker algorithms which can only reproduce wave motions either of periodic or of constant form. A series of laboratory experiments is described where relatively arbitrary single waves are specified as initial data, the theory calculates the correct boundary motion, the waves are generated and then compared with the initial data as a...

Forces on Vertical Wall Caused by Incident Bores

Abstract: The forces on a vertical wall due to the impact of a bore generated by a broken solitary wave were measured in the laboratory. The bores varied in height from 3.1 - 4.9 cm and in celerity from 75 - 126 cm/s. High-speed motion pictures of the bore impact process were taken simultaneously with force measurements. The water particle velocities on the surface of the bore were obtained from the motion pictures using small floats. The maximum rise of the water surface on the wall exceeded twice the velocity head, based on the bore celerity for all conditions. The maximum measured force occurred after the maximum run-up for all conditions of this study. The vertical accelerations in the run-up jet at the wall explain some of the characteristics of the force record that have not been well understood. The maximum measured forces varied from five to nearly seven times the hydrostatic force, based on the height of the incident bore and the local still-water depth. For the four largest bores, the theory of Cross (1967) was in reasonable agreement with the maximum measured force.

Accretion behind single offshore breakwater

Abstract: This study notes that the main variables in evaluating apex postion of a salient behind a single breakwater parallel to the shore with waves normal to both are its length and distance offshore. Because the shape of the salient is related to wave diffraction patterns, the apex distance from the breakwater on its centerline, its radial distance, and angle from the tip of the breakwater are all useful measurements when related to the two main variables mentioned. It is also noted that values of breakwater length to distance offshore have been established for the limting conditions of tombolo and zero salient formation. Between these two extremities, the extent of salient accumulation in equilibrium state can be determined quantitatively for designing a single offshore breakwater.

Irregular Wave Reflection and Run‐Up on Rough Impermeable Slopes

Abstract: Three irregular wave test runs were conducted to obtain detailed data on irregular wave reflection and run-up on a 1:3 rough impermeable slope. The test results were also used to evaluate the capabilities and limitations of an extended numerical model for predicting the time series and spectral characteristics of the reflected waves and waterline oscillations on the slope. The numerical model is shown to predict the measured time series and spectra reasonably well, including the selective nature of wave reflection and dissipation as well as the appearance of low-frequency wave components in the waterline oscillations on the 1:3 slope. The numerical model extended herein may not be as accurate as hydraulic model tests but can be used to predict hydrodynamic quantities that are difficult to measure directly. Moreover, any incident irregular wave train including that measured in the field or generated numerically for given incident wave spectrum can be specified as input to the numerical model. This will avoid the difficulties associated with the reproduction of specified incident irregular waves in experiments.

2‐D Bed Evolution in Natural Watercourses—New Simulation Approach

Abstract: A new mathematical formulation is established for two-dimensional (plan view) unsteady water flow, sediment transport, and bed evolution in natural watercourses such as reservoirs, estuaries, coastal water where depth averaging is appropriate. Sediment mixtures in natural watercourses are represented through a suitable, and unlimited, number of discrete size classes, any of which may be subject to either suspended-load or bedload transport (or both) depending on prevailing local hydraulic conditions. Governing equations for water and sediment are transformed (completely) into curvilinear coordinates and then depth-averaged, when appropriate. The system of governing sediment equations at a computational point is solved in a new implicit, finite-difference, fully coupled manner. Furthermore, the sediment equations are coupled with the water flow in an iterative manner in order to account for the feedback between the flow field and changes in both bed elevation and bed-surface size distribution. The mathematical formulation and associated numerical solution, incorporated into the new MOBED2 computational code, are tested through simulation of mobile-bed dynamics in the Coralville Reservoir on the Iowa River, Iowa. Initial proof-of-concept tests confirm the feasibility of the new approach by reproducing the proper qualitative behavior of the overall modeling concept.

Numerical Simulation of Irregular Wave Propagation over Shoal

Abstract: 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 us...

Nonlinear effects on wave envelope and phase

Abstract: The effects of second‐order nonlinearities on the envelope and phase statistics of long‐crested sea waves are examined theoretically via the characteristic function expansion technique. Various cumulants typically required in this technique are derived explicitly to the first order of accuracy in the spectral bandwidth of sea surface elevations. The resulting joint and marginal probability densities are then examined in detail and checked with simulations. It is found that, except for certain minor modifications, the statistical distribution of envelope heights normalized by their rms‐value is described on the whole fairly well by the conventional Rayleigh law. In comparison, the wave phase and phase statistics are affected more significantly by nonlinearities, showing a systematic excess of values near the mean phase. The eventual comparison of the theoretical predictions with the actual wave data gathered from an offshore platform in the Gulf of Mexico in 1969 supports these conclusions surprisingly wel...

Influence of wind on breaking waves

Abstract: The influence of local wind on nearshore breaking waves was investigated in a laboratory wave‐wind flume. The breaker location, geometry, and type were found to depend strongly upon the wind direction. Onshore winds cause waves to break earlier, to break in deeper water farther from shore, and to spill; offshore winds cause waves to break later, to break in shallower water closer to shore, and to plunge. For onshore winds, it was observed that breaking of the wind‐generated ripples can initiate spilling breaking of the primary underlying wave by providing a perturbation on the crest of the underlying wave as it shoals. The implications of these results are that surf zone width, currents, and sediment transport can be affected by local winds. Thus, engineering estimates of these quantities could be improved by consideration of local wind. Surf zone dynamics models that ignore wind or include wind only as a surface shear may be missing a very important effect of the wind—its effect on the initiation and mec...

Optimum Allocation and Size of Seaports

Abstract: The amount of general cargo that is transported through public wharves in a port is not necessarily constant for a certain period of time; it will change depending on the relative location of the port to other ports in a country. In this paper, a method to determine the optimum allocation and size of ports in a country is proposed from a national economic point of view. The total cost spent in transporting general cargo consists of two kinds of costs; i.e., the total inland transportation cost and the total port cost. The former cost is a linear function of the amount of cargo transpoted; while the latter cost is a nonlinear function and is not easy to treat. Consequently, the total port cost is approximated by a piecewise linear function. Thus, the application of the separable programming technique to this type of allocation problem has proved successful. The optimum berth planning of ports in a country can be executed efficiently and easily with the aid of the procedures herein developed.

Longshore‐Transport Model for South Indian and Sri Lankan Coasts

Abstract: Longshore-sediment transport rates for the south Indian coast from Allur to Cochin and for Sri Lanka are estimated from ship-reported wave data (1968–86). Annual gross sediment transport rate is high (1.5 to 2.0 × 10\u6 m³) along the coasts of north Tamil Nadu and south Kerala and is less (0.5 to 1.0 × 10\u6 m³) along the south Tamil Nadu and Sri Lankan coasts. The annual net transport is southerly along the west coast of India and predominantly northerly along the east coast except near Durgarajupatnam in Andhra Pradesh. Coasts near Tharangampadi, Karaikal, Nagore, Tuticorin, Virapandianpatinam, and Manakkodam in Indian and Kuchchaveli, Betticola, Pottuvil, Chilaw, and Negombo in Sri Lanka appear to be nodal drift points, with an equal volume of transport in either direction annually.

Simulation of Nonstationary, Non‐Gaussian Water Levels on Great Lakes

Abstract: A methodology for simulating nonstationary non-Gaussian water levels on the Great Lakes is presented for use in providing input scenarios for erosion modeling on the Great Lakes. The methodology utilizes a low-pass filtering technique to reduce the data to a stationary time series after which the data is transformed to a Gaussian series via use of the empirical distribution function coupled with a specialized tail-fitting procedure for the extreme values in the data. The reduced series can then be resimulated in the frequency or time domain. The present series is resimulated in the frequency domain via a target spectrum, the spectrum of the reduced series. Inverse procedures are then utilized to simulate the original series. Comparisons of statistical and time series properties of the original and simulated series are made for a number of sites on the Great Lakes and it is found that the methodology provides a reasonable simulation for the original data.

Time‐Domain Solution for Second‐Order Wave Diffraction

Abstract: A numerical method for calculating the transient, second‐order interaction of ocean waves with large fixed offshore structures of arbitrary shape is described. The development of the flow together with the associated fluid forces is obtained by a time‐stepping procedure in which the flow at each time step is calculated by an integral‐equation method based on Green's theorem. The nonlinear free‐surface boundary conditions and Green's theorem defined on the instantaneous free surface are first expanded about the still‐water level by a Taylor series expansion and terms up to second order are retained through a perturbation procedure. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. The procedure is applied to the two‐dimensional, vertical‐plane case of a submerged circular cylinder subjected to regular incident waves. Comparisons with a previous second‐order theory and a previous experimental study are presented and indi...

Diffraction of Long Waves by Rectangular Pit

Abstract: Linearized shallow water wave theory is utilized to investigate the interaction of surface waves with a rectangular pit of finite dimensions in water of otherwise uniform depth. The fluid domain is divided into two regions: an interior region whose boundary consists of the projection of the outline of the pit and an exterior region consisting of the remainder of the fluid domain. Application of Green's second identity utilizing an appropriate Green's function in each region leads to a pair of simultaneous integral equations for the velocity potential and its normal derivative at the imaginary fluid interface between the two regions. These integral equations may then be discretized and the resulting systems of algebraic equations solved by standard matrix techniques. Utilizing the values of the velocity potential and its derivative on the imaginary fluid boundary, a reapplication of Green's identity allows the potential at any point in the fluid to be determined. Based on this solution technique, numerical...

Practical application of theory for tidal-intrusion fronts

Abstract: 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 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.

FRF Spectrum: TMA with Kitaigorodskii's f-4 Scaling

Abstract: This paper describes the development of a mathematical function which represents the spectrum of wind-generated gravity waves in water of arbitrary depth. The derivation parallels that of the TAM spectrum. The primary difference is that Philips' (1958) model for saturation at high frequencies is replaced by Kitaigorodskii's (1983) model. This spectrum incorporates wind speed directly into the formulation and is consistent with an fE-4 power law scaling for deep water. In its raw form the new model requires four internal constraints (gravity, depth, wind speed and peak frequency), and has four model coefficients. Values for the coefficients are determined for 1,022 observations of wave spectra made at the Corps of Engineers Field Research Facility (FRF) in depths of 19, 8.5 and 6m. The coefficients are then correlated with dimensionless combinations of the physical parameters associated with the spectrum to see if the number of coefficients can be reduced. If three of the coefficients are held constant at their mean values, a direct relationship to wave steepness is obtained for the forth coefficient that is related to the peakedness of the spectrum.

Scheduling Maintenance Dredging on Single Reach with Uncertainty

Abstract: New methods are suggested for scheduling advance maintenance dredging on isolated reaches of navigation channels based on economic and reliability analysis. For reaches where sedimentation occurs regularly as a result of gradual slumping, quiescent deposition, or regular erosion due to waves and wakes, the problem reduces to a deterministic least-cost replacement problem. Where sedimentation rates are uncertain, the risk of sediment encroachment into the navigational channel becomes a concern. Where sedimentation rates are probabilistic and independently distributed in time, encroachment probabilities and expected dredging costs can be calculated for a variety of dredging schedules. This risk and cost analysis allows explicit specification of risk-cost trade-offs in dredge scheduling. These methods are applied to an example case where existing dredging costs are compared with those estimated using these new dredge scheduling techniques. Extensions of these methods could be applied to multiple-reach dredge scheduling, sizing sediment traps, and scheduling dredging with explicit consideration of environmental impacts.

Wave‐Induced Breakout of Half‐Buried Marine Pipes

Abstract: An experimental study is conducted in order to identify the major physical processes leading to the breakout of half‐buried submarine pipelines from the seafloor under ocean‐wave action. Both the hydrodynamic loading on the exposed surface of the pipe as well as the pore‐pressure distribution on the buried surface were measured. The resulting displacement histories of the pipe were recorded and analyzed in order to identify the critical pipe‐soil‐wave conditions for the detachment of the pipe from the seabed. The paper examines the balance of the pipe under the combined lift and drag loading from the water wave. The experimental coefficients of drag, lift, and added mass have been calculated by the least squares method and compared with theoretical predictions. As for the soil response, a simple theoretical model is worked out to describe the pore‐pressure resistance force at the soil‐pipe interface. An experimental breakout force‐time power law is obtained and compared with the theoretical model.

Analytical design method for relatively closed block revetments

Abstract: A semianalytical, semiempirical method is developed to compute the loads on and the strength of a placed block revetment under perpendicular wave attack. The method consists of an empirical computation of the external wave loads on the revetment and an analytical method to calculate the internal hydraulic loads in the sublayers of the slope protection structure. Together, the internal and the external loads determine the resulting pressure differences across the top layer. The strength of the top layer is treated as the sum of the weight of the block revetment and a number of additional strength factors: the friction between adjacent blocks, the inertia of a block when it becomes unstable, and the pressure drop underneath an unstable, ejecting block. These additional strength factors are quantified analytically and are verified separately by means of extensive experimental model testing on a prototype scale. The method as a whole is verified by means of large‐scale model tests in a large wave flume, where...

Viscous Damping of Cnoidal Waves Over Fluid‐Mud Seabed

Abstract: The heights of water waves propagating over fluid-mud bottom can be significantly reduced due to the viscous energy dissipation occurring in the mud bottom. In some cases, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths. This phenomenon has been observed both in field investigation and in laboratory experiment action. In this paper, the viscous damping of cnoidal waves progressing over fluid-mud seabeds is investigated, in which fluid mud is assumed to be a viscous fluid. The theoretical model adopted here is a two-layer viscous fluid model modified with three boundary layers at the water-mud interface and at the rigid bottom beneath mud layer. Viscosities of both water and fluid mud are taken into consideration. For a nonlinear shallow wave progressing over a viscous mud bed, the first-order analytical solutions are derived for the velocity distributions in boundary layers and for the attenuation rate of wave heights with distance. The attenuation coefficients are larger than those predicted on the basis of linear shallow wave theory and unlike the case of linear shallow waves, they are not independent of wave height. The viscous damping of solitary and sinusoidal waves, which are two extreme cases of cnoidal wave, are also discussed according to the present solution.

Salinity Changes in Charleston Harbor 1922-1987

Abstract: Charleston Harbor, South Carolina, has undergone pronounced changes in salinity regimes because of the diversion of the Santee River into the Cooper River in 1942 and rediversion of the Cooper into the Santee in 1985. The mean monthly harbor surface salinity changed from 30.1 ppt to 16.8 ppt as a result of the diversion, and has again increased to 22.0 ppt since rediversion. Postdiversion monthly mean Cooper River discharge was 418m3s-1, but since rediversion, the monthly mean discharge has decreased to 122m3s-1 and become less variable. Regression models for salinity variability in Charleston Harbor and Cooper River have been developed. Based on these models, discharge alone explains 78% of the salinity variance during the postdiversion period, but accounts for only 1% of the salinity variance after rediversion because of the near constant discharge. Thus, the estuary is presently much more susceptible to salinity changes due to far‐field forcing from the coastal ocean.

Response of Finite Depth Seabed to Waves and Caisson Motion

Abstract: The response of a poroelastic seabed to waves and caisson motion is modeled using Biot consolidation theory. The caisson is founded on a rubble bedding layer overlying a seabed of finite depth. Two approximations are employed to solve the boundary-value problem analytically: (1) A boundary layer approximation to decouple pore pressure and soil motion in the Biot equations; and (2) a contact solution approximation for a thin elastic layer to address the mixed-type mud line condition. The analytical solution is verified by comparison with finite element model results and large-scale experiments. The analytical and finite element model estimates of the soil stresses and surface displacements are in good agreement. Experimental and analytical comparisons for pore pressure are in agreement but the displacement comparisons are quite scattered.

Effects of Opposing Waves on Momentum Jets

Abstract: In an earlier work, Ismail and Wiegel (1983) observed experimentally that due to the effects of opposing waves, the spreading rates of a momentum jet are increased. They argued that the increases are caused by the radiation stresses generated by waves. Through numerical computations, the effects of opposing waves on momentum jets are reexamined in this paper. It is found that the radiation shear stress components Sxy indeed increase the jet width. However, the radiation normal stress Sxx actually decreases the jet width. The combined effects of both radiation stress components reduce the jet width. The true mechanism for increasing the jet width is due to the increase of bottom friction and turbulent intensity as the results of the wave and current interactions.

Random wave forces near free surface

Abstract: The paper describes random wave forces acting on a slender structural member in the vicinity of the water surface, taking account of the intermittency of submergence. A brief review is initially given of available formulations for fully submerged portions of a member, these being based on the Morison equation applied in conjunction with linear wave theory. The Morison equation is generally linearised in order to estimate spectral densities, while its nonlinearity is retained in order to estimate probability densities and consequently extreme force values. For section located near the free surface, the intermittency of submergence drastically alters the statistics of the water particle kinematics in the random wave field end consequently those of the wave forces. Expressions for the spectral density of the force and the probability density of the force maxima are derived. Numerical results relating to these and to the vertical distribution of extreme forces are presented, and the effects of including the intermittent submergence near the free surface are illustrated.

High‐Wave‐Number/Frequency Attenuation of Wind‐Wave Spectra

Abstract: 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. 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...

Wave radiation by truncated elliptical cylinder

Abstract: The radiation of small-amplitude water waves by an oscillating submerged elliptical cylinder is investigated analytically. The cylinder may either be totally submerged and resting on the seabed (case I) or partially immersed in the free surface (case II). The fluid domain is divided into two regions: an interior region about (Case I) or below (case II) the structure and an exterior region extending to infinity in the horizontal plane. Expressing the boundary-value problem in elliptical coordinates, analytical expressions for the velocity potentials satisfying the governing equation and boundary conditions in each region may be written in terms of infinite series involving Mathieu and modified Mathieu functions. The unknown coefficients in these series are determined by imposing continuity of mass and momentum fluxes at the fluid interface between the two regions. Utilizing this solution, numerical results are presented that illustrate the variation of the added-mass and radiation damping coefficients with oscillation frequency for several example structures.

North Sea Bottom Steady Boundary Layer Measurements

Abstract: The steady-flow boundary layer was studied with measurements of tidal current and wave velocity made at 0.10, 0.25, 0.50, 1.00, 3.00, and 5.00 m above the sea floor at two locations in the North Sea in 70-m and 102-m water depths. The data cover a range of combined current and wave conditions. The logarithmic boundary-layer flow model was successfully fitted to the current measurements using the roughness \Iz\N\d0 and friction velocity \Iu\N\u〈 as fitting parameters. The measurements and analysis results demonstrate the existence of large boundary-layer current gradients in typical offshore locations and large values of \Iz\N\d0 and \Iu\N\u〈. They also show the dependence of these parameters on the ratio of wave flow to the current flow component as well as the bottom roughness. The measurements further demonstrate that the boundary-layer profile can vary greatly for the same general location due to movable bottom effects and general ocean turbulence. Theoretical model predictions for the wave-current interaction effect and the movable bottom effects showed limited success. The findings here can be used to estimate hydrodynamic forces on marine pipelines.