Showing papers in "Journal of Waterway Port Coastal and Ocean Engineering-asce in 1998"

Numerical Modeling of Tidal Wave Runup

Abstract: A numerical solution for the 2 + 1 (long-shore and onshore propagation directions and time) nonlinear shallow-water wave equations, without friction factors or artificial viscosity is presented. The models use a splitting method to generate two 1 + 1 propagation problems, one in the onshore and the other in long-shore direction. Both are solved in characteristic form using the method of characteristics. A shoreline algorithm is implemented, which is the generalization of the earlier 1 + 1 algorithm used in the code VTCS-2. The model is validated using large-scale laboratory data from solitary wave experiments attacking a conical island. The method is applied then to model the 1993 Okushiri, Japan, the 1994 Kuril Island, Russia, and the 1996 Chimbote, Peru tsunamis. It is found that the model can reproduce correctly overland flow and even extreme events such as the 30-m runup and the 20-m/s inundation velocities inferred during field surveys. The results suggest that bathymetric and topographic resolution ...

Wavemaker Curves for Tsunamis Generated by Underwater Landslides

Abstract: A nondimensional wavemaker curve of a characteristic water wave amplitude is constructed from the landslide length, the initial landslide submergence, the incline angle measured from the horizontal, the characteristic distance of landslide motion, and the characteristic duration of landslide motion. This wavemaker curve applies broadly to water waves generated by unsteady motion of a submerged object, provided the motion is governed by only one characteristic distance scale and one characteristic time scale. An analytical solution of solid block motion provides the characteristic distance scale and time scale. Two-dimensional experimental results on a 45° incline confirm that a wavemaker curve for solid block landslides exists as a function of the nondimensional initial submergence and what is called the Hammack number. Water wave amplitudes generated by solid block landslides can be predicted from the wavemaker curve if the solid block motion is known. Criteria for the generation of linear water waves are given.

Wave Interactions with Vertical Slotted Barrier

Abstract: The present paper outlines the numerical calculation of wave interactions with a thin vertical slotted barrier extending from the water surface to some distance above the seabed, and describes laboratory tests undertaken to assess the numerical model. The numerical model is based on an eigenfunction expansion method and utilizes a boundary condition at the barrier surface that accounts for energy dissipation within the barrier. Numerical results compare well with previous predictions for the limiting cases of an impermeable barrier and a permeable barrier extending down to the seabed. Comparisons with experimental measurements of the transmission, reflection, and energy dissipation coefficients for a partially submerged slotted barrier show good agreement provided certain empirical coefficients of the model are suitably chosen, and indicate that the numerical method is able to account adequately for the energy dissipation by the barrier. The effects of porosity, relative wave length, wave steepness, and irregular waves are discussed and the choice of suitable parameters needed to model the permeability of the breakwater is described.

Numerical Model of Wave Run-Up, Overtopping, and Regeneration

Abstract: A numerical model of wave run-up, overtopping, and regeneration is presented. The model (called OTT) is based on the one-dimensional nonlinear shallow water equations on a sloping bed, including the effects of bed shear stress. These equation are solved using a finite-volume technique incorporating a Roe-type Riemann solver. The main advantage of this approach over previously used finite difference solvers is that no special shoreline-tracking algorithm is required, so that noncontiguous flows can easily be simulated. Hence, this model can be used to simulate the transmission of waves over water surface-piercing obstacles. The numerical scheme and boundary conditions are described, and several existing data sets used to test the ability of the model to simulate wave transformation, run-up, and overtopping. Experiments of random wave (unimodal and bimodal) overtopping, presented here for the first time, indicate that the model performs much better than empirical formulas in predicting average overtopping rates, and that it provides good estimates for the number of overtopping events. Experiments of overtopping of a sea wall by solitary wave are also presented, including measurements of wave regeneration in lee of the dike. The model does a reasonable job of reproducing the water depths on top of the dike, and performs well in simulating the initial height of the regenerated waves.

Wave scour around group of vertical piles

Abstract: The paper presents the results of an experimental investigation on scour around pile groups with different configurations exposed to waves. Two kinds of tests were carried out: the actual scour experiments, and bed shear stress measurements. Seven kinds of pile-group arrangements were tested, including the side-by-side arrangements of piles, tandem arrangements of piles, and triangular and square group arrangements with two-, three-, and four-pile groups. The variations with the pile spacing as well as the Keulegan-Carpenter number, \IKC\N, were investigated. The scour depth can increase with respect to its single-pile value by as much as a factor of 3 for moderate \IKC\N numbers [such as \iO(10)] for most of the pile-group configurations for small pile spacings. For small \IKC\N numbers, this increase can be even higher, by as much as a factor of 10 or more. For a given pile spacing, the scour depth is mainly governed by the \IKC\N number. In agreement with the single-pile case, the larger the \IKC\N number, the larger the scour depth. The bed was live in all the tests except a few cases.

Experiments on Nonlinear Wave Groups in Intermediate Water Depth

Abstract: Evolution of nonlinear wave groups of various initial envelope shapes is studied experimentally in a wave tank. Experiments are performed for different values of the water depth in the tank. The experimental results are compared with the calculations based on the cubic Schrodinger equation. Qualitatively different results are obtained for water depth values corresponding to different signs of the nonlinear term coefficient in the model equation. In relatively shallow water, the demodulation of wave groups is observed, while in a deeper water the maximum wave height increases along the tank due to the focusing, as expected.

Spectral Model for Wave Transformation and Breaking Over Irregular Bathymetry

Abstract: A numerical model is presented that predicts the evolution of a directional spectral sea state over a varying bathymetry using superposition of results of a parabolic monochromatic wave model run for each initial frequency-direction component. The model predicts dissipation due to wave breaking using a statistical breaking model and has been tested with existing data for unidirectional random waves breaking over a plane beach. Experiments were also conducted for a series of random directional waves breaking over a circular shoal to test the model in a two-dimensional wave field. The model performs well in both cases, although directional effects are not included in the breaking dissipation formulation.

Estimating Wave Heights from Pressure Measured in Sand Bed

Abstract: Comparison of predicted with observed attenuation of pressure fluctuations shows that wave heights can be estimated with observations from a pressure sensor that is buried a known depth in fine sand. The attenuation of pressure fluctuations within the sand bed under unbroken shoaling waves, bores in the surf zone, and swash near the shoreline was measured with vertical stacks of buried pressure sensors. The attenuation increased with increasing frequency and depth below the bed surface, consistent with previous observations under nonbreaking waves in deeper water and with model predictions based on poro-elastic theory. In the limit of an infinitely deep soil skeleton that is much more compressible than the pore fluid, the predicted pressure fluctuations decrease exponentially with increasing burial depth, and the attenuation is independent of the sediment properties. For the fine-grained sand beds considered here, this exponential limit accurately predicts the observed attenuation.

Hydrodynamic Interactions of Waves with Group of Truncated Vertical Cylinders

Abstract: An exact analytical method is described to solve the diffraction and radiation problems of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilized. The isolated cylinder diffraction and radiation potentials are obtained using Garret's solution, and evanescent mode solutions are derived in a similar manner. Numerical results are presented for arrays of two and four cylinders. Comparisons between the results obtained from the method presented here and those obtained from numerical methods show excellent agreement.

Probability distribution of surface elevation in surf and swash zones

Abstract: Three irregular wave tests were conducted on a 1:16 smooth impermeable slope to investigate the detailed cross-shore variations of the probability distributions and statistics of the free surface elevations and middepth horizontal velocities in the shoaling, surf, and swash zones. The exponential gamma distribution with the measured mean, standard deviation, and skewness is shown to be capable of describing the measured probability distributions in a unified manner, although the agreement becomes worse in the lower swash zone. The probability distribution of the free surface elevation whose lower limit is imposed by the beach face in the swash zone becomes exponential with the skewness s= 2 and the standard deviation σ=h¯ with h¯= mean water depth. These upper limits of s and σ/h¯ in the lower swash zone are in qualitative agreement with the data in the region of h¯≳ 0.4 cm in these small-scale tests. The cross-shore variations of the mean (undertow) and standard deviation of the middepth horizontal veloc...

Residence Time of Freshwater in Boston's Inner Harbor

Abstract: Two field tracer studies and some numerical model experiments were used to analyze the residence time of freshwater in Boston's inner harbor, and thereby help evaluate water quality impacts of combined sewer overflows. An exponential filter was used to modify the freshwater fraction approach for variable freshwater inflow and to reanalyze data from Bumpus et al. (1953). Results showed an inverse relationship between residence time and inflow rate, with times ranging from 2 to 10 d. An instantaneous dye study gave a residence time of 3.75 d, consistent with the freshwater measurements for conditions of summertime low flow. A three-dimensional (3D) numerical model applied to a schematized domain was able to reproduce trends observed in both the freshwater and dye studies.

Wave phase shift at coastal structures

Abstract: Wave reflection from coastal structures is defined by the magnitude and phase of the reflected wave. Both properties have a profound impact on the wave kinematics and coastal processes in front of the structure. This paper focuses on the phase shift on reflection. Using a large experimental data set, involving normally incident and obliquely incident regular and irregular waves, it is shown that the phase is uniquely determined by a nondimensional number χ\d3 defined by structure slope, water depth at the structure toe, wave period, and angle of incidence. A theoretical method for predicting phase shift based on matching the equation for linear long waves on a sloping beach with an equation for flat-bed standing waves seaward of the structure toe yields good estimates of the phase shift at low values of χ\d3. A second method based on integration of the shallow water wave number over the slope is considered and not recommended. Example cases are presented that demonstrate the practical importance of the phase shift in determining the kinematics in front of the structure.

Coastal Flood Risk Assessment

Abstract: In many parts of the world, design standards now require the assessment of risks. Measures of risk are often qualitative, with descriptors such as “high,”“low,”“intolerable,” or “negligible.” The practitioner is thus left with the task of reconciling the qualitative assessment of risks with the quantitative demands of design. Probabilistic techniques are being used increasingly for the design and assessment of sea defenses. In this paper the use of probabilistic techniques in risk assessment for sea defenses is considered. The respective advantages and disadvantages of different techniques are discussed. Some new approximate methods are described and compared with existing approaches. Example calculations based on 21 years of synthesized wave and water level data are presented for the case of wave overtopping. The different methods are employed to calculate the probabilities of exceeding the overtopping threshold for two structures. The results are used to discuss what might be considered practical and re...

Integrated control for series of waterway locks

Abstract: Delays in a waterway network are affected by tow arrival characteristics, service time distributions, lock characteristics, and control policies at locks. Previous studies have shown how interdependence among locks in a series complicates the delay estimation. Among control policies, “shortest processing time first” (SPF) yields lower delays and costs per barge than the generally used “first come, first served” (FCFS) policy. This report considers the interdependencies among locks in an integrated control algorithm for series of locks. The results show that an integrated control algorithm yields lower costs per barge for both FCFS and SPF control, with either equal or unequal directional flows. A modified SPF control that considers delays at adjacent locks (SPF&A) yields the lowest costs per barge among all control alternatives considered. The results show how the interdependence between locks decreases and delays increase as the distance between locks increases.

Flexible Dual Membrane Wave Barrier

Abstract: This paper discusses the performance of a wave barrier consisting of two vertical flexible membranes spaced at a fixed distance apart. The interaction of the membrane system with uniform incident water waves is investigated within the context of two-dimensional linear wave theory. The membranes extend the entire water depth and are tensioned and pinned at both the surface and the seabed. Analytic solutions are developed using eigenfunction expansions for the velocity potential and linear membrane theory. It is found that the transmission and reflection characteristics are highly sensitive to the membrane spacing and tension. These parameters offer the opportunity to tune the barrier system for achieving low energy transmission at a lower membrane tension as compared with a single membrane, and to reflect waves over selected frequency bands. Additional reductions in the transmitted wave energy from viscoelastic dissipation within the membrane are found to be small.

Longshore Sediment Flux in Water Column and Across Surf Zone

Abstract: Streamer sediment traps were used to measure the distribution of longshore sediment flux in the surf zone at 29 locations along the southeast coast of the United States and the Gulf coast of Florida Measurements were conducted on both barred and nonbarred coasts under low-wave energy conditions Results indicate that longshore sediment flux decreases logarithmically upward in the water column throughout the surf zone, and the rate of upward decrease is largest in the trough and smallest in the swash due to stronger mixing energy in the swash Six types of cross-shore distribution patterns of longshore sediment transport (LST) were found These six distribution patterns are controlled by nearshore morphology, breaker type, and energy dissipation pattern For low-wave energy coasts, the swash (nonbarred coast) and inner surf (barred coast) zones contain significant contributions to the longshore sediment transport rate The cross-shore distribution pattern of the longshore sediment transport rate along nonbarred coasts was well reproduced using energy-dissipation and shear-stress approaches developed mainly from laboratory studies

Dynamical Models for Cross-Shore Transport and Equilibrium Bottom Profiles

Abstract: The long-term cross-shore dynamics of the surf zone affected by storms is investigated. The validity of the hypothesis of equilibrium bottom profiles in the coastal zone is examined using bathymetric measurements of some coastal regions in Israel for the period 1968–1995. It is shown that the power law of depth variation as a function of offshore coordinate (Dean's profile) is satisfied on the average for nonbarred profiles. Bar development for the period of the last five years is analyzed. A mathematical model for description of time-dependent sea bottom deformation under the action of wind waves in the surf zone is developed. It is found that, besides the known static solutions of the balance equation for sediment transport, which correspond to the equilibrium bottom profile with zero net sediment transport, there exists a solution corresponding to the profiles of dynamic equilibrium when the surf zone is a “carrier” of sediment transport from the coast to the sea or in the opposite direction. Both equi...

Performance of Dual Flexible Membrane Wave Barriers in Oblique Waves

Abstract: The interaction of oblique incident waves with a dual vertical-flexible-membrane wave barrier hinged at the seafloor is investigated in the context of two-dimensional linear wave-body interaction theory. First, analytic solutions for an idealized system without a buoy are obtained as a benchmark result. Second, a more practical system with the membrane tension provided by a buoy at its top is investigated by the three-domain boundary element method (BEM) particularly devised for dual membrane problems. For each case, both submerged and surface-piercing systems were considered. The BEM program is developed based on a discrete membrane dynamic model and simple-source (second-kind modified Bessel function) distribution over the entire fluid boundaries. Because the boundary condition on the membrane is not known in advance, the membrane motions and velocity potentials in each region are solved simultaneously. The accuracy and convergence of the numerical method are checked against the energy-conservation formula and further verified through comparison with analytic solutions in case the size of a buoy is infinitely small. Using the developed computer program, the performance of surface-piercing or submerged dual membrane wave barriers is tested with various system parameters and wave characteristics. It is found that the efficiency of a dual membrane breakwater can be significantly enhanced compared to the single membrane case if it is properly designed. It is also found that the asymmetric system can function better then the symmetric system through desirable tuning.

Two Dimensional Parabolic Modeling of Extended Boussinesq Equations

Abstract: A frequency domain wave transformation model is derived from a set of time-dependent extended Boussinesq equations. In contrast to an earlier study, this model is derived directly from the (η, u) form of the equations. The resulting model maintains the excellent dispersive properties of the original equations and also accurately mimics the shoaling behavior of dispersive linear theory for a wide range of water depths. The model is formulated in terms of a free parameter that can be tuned for optimum shoaling behavior. We tune the parameter in two ways; the first seeks the minimum error for the shoaling parameter while using the optimum value for the dispersion parameter, while the second seeks the minimum combined error for both dispersion and shoaling. These lead to two different sets of free parameters, with the second method leading to more favorable linear shoaling behavior than the first. The effectiveness of the linear terms of the model is demonstrated by using them, with both sets of free paramete...

Mechanism for formation of lutoclines by waves

Abstract: The mechanism by which a suspended fine-sediment-induced pycnocline, or lutocline, is generated under wave action is examined. The steady-state form of the turbulent kinetic energy balance is used along with commonly invoked phenomenological arguments to obtain a formula for the height of the lutocline as a function of wave and suspended sediment properties. This formula is then used in conjunction with data on equilibrium heights of lutoclines of a suspended clay mixture in a wave flume to show that the formula holds promise as a first-order predictor of lutocline height. This height is also shown to correlate empirically with wave energy.

Bed Forms Generated on Sandy Bottom by Oblique Standing Waves

Abstract: This paper presents the results of a study of bed forms generated on a sandy bottom by an oblique standing wave resulting from obliquely incident long-crested waves on a fully reflecting vertical wall. Under antinodes of the oblique standing wave, the sand ripples have crests aligned perpendicular to the wall (type A); under nodes, the ripple crests are aligned with the wall and ride on the top of larger scale sandbars (type C), whereas “island” ripples of a honeycombed structure (type B) appear between nodes and antinodes of the oblique standing wave system. The type A and C ripples could be compared to those generated by long-crested progressive waves, whereas the sandbars at nodes, with ripples riding on them, were compared to those generated by two-dimensional standing waves. Results for the bed-form geometry of type A ripples, type C ripples, and sandbars, as well as type B “bottom islands,” are presented as a function of water particle semiexcursion, mobility number, and Shields parameter.

Effects of Sediment Transport on Bed Friction and Turbulence

Abstract: The effects of sediment transport on the fluid velocities and turbulence in oscillatory flow were investigated with the aid of a laser Doppler anemometer (LDA). Measurements were made over flat beds in an oscillatory flow water tunnel with gradually increasing quantities of sediment. The sediment had a specific gravity of 1.137 and a median diameter of 4.0 mm. It was observed that the turbulence intensity at any given height above the initial bed level was less in flows with sediment motion than over a fixed bed provided the bed remained flat. The initial bed level is defined as the mean grain crest level if all sediment settles on the bed. The friction factor and energy dissipation factor at the initial bed level were also reduced by the addition of sediment provided the bed remained flat. On the other hand, the values of friction factor and energy dissipation factor at the bottom of the mobile layer of sediment were greater than the values for a fixed bed.

Velocity parameters for predicting cross-shore sediment movement

Abstract: This paper discusses a method to estimate the tendency of sediment to move onshore or offshore under the influence of waves in shallow water. Motivation for this study is provided by the need for conceptually simple models to help explain the movement of noncohesive sediments under waves, especially cross-shore transport. Two dimensionless velocity parameters are developed to predict the tendency of sediment to move onshore under wave crests or offshore under troughs. The parameters are the ratio of the instantaneous, maximum near-bottom velocity under a wave crest or trough to the critical velocity for the initiation of sediment movement. Near-bottom velocities are estimated using stream function wave theory. One parameter shows considerable skill in predicting net cross-shore sediment movement for a large number of observations of laboratory and field beaches. Taken together, the two parameters provide a qualitative explanation for observed movement of a submerged gravel mound. Previous studies indicate that wave asymmetry can cause net onshore sediment move­ ment and undertow can cause net offshore movement in the surf zone. The utility of these parameters also is examined for mounds composed of dredged material. where U-dmu = near-bottom velocity produced by waves; and Ucrit = critical velocity required to initiate sediment movement. 1\vo versions of V are used in this paper, Vc and V" which are associated, respectively, with the instantaneous maximum onshore velocity under the crest and the instantaneous maxi­ mum offshore velocity under the trough. ABSTRACT: This paper discusses a method to estimate the tendency of sediment to move onshore or offshore under the influence of waves in shallow water. Motivation for this study is provided by the need for conceptually simple models to help explain the movement of noncohesive sediments under waves, especially cross-shore transport. Two dimensionless velocity parameters are developed to predict the tendency of sediment to move onshore under wave crests or offshore under troughs. The parameters are the ratio of the instantaneous, maximum near-bottom velocity under a wave crest or trough to the critical velocity for the initiation of sediment movement. Near-bottom velocities are estimated using stream function wave theory. One parameter shows considerable skill in predicting net cross-shore sediment movement for a large number of observations of laboratory and field beaches. Taken together, the two parameters provide a qualitative explanation for observed movement of a submerged gravel mound. Previous studies indicate that wave asymmetry can cause net onshore sediment move­ ment and undertow can cause net offshore movement in the surf zone. The utility of these parameters also is examined for mounds composed of dredged material. where U-dmu = near-bottom velocity produced by waves; and Ucrit = critical velocity required to initiate sediment movement. 1\vo versions of V are used in this paper, Vc and V" which are associated, respectively, with the instantaneous maximum onshore velocity under the crest and the instantaneous maxi­ mum offshore velocity under the trough.

Initial Motion of Sediment in Oscillatory Flow

Abstract: A new model is developed to study the initial motion of sediment in oscillatory flow over a flat bottom on the basis of available experimental data. It is found that the initial motion of sediment in oscillatory flow is uniquely defined by the simple model of A/d=KA2ω/ν+B, where A= semiexcursion of wave orbital motion near the bed; ω= angular frequency; d= grain diameter; ν= kinematic viscosity; and K and B= dimensionless coefficients determined by the immersed sediment weight. For a given sediment, the onset velocity derived from the model is found to initially increase with the wave period T and then approach a constant. A practical formula is also presented to calculate the onset velocity of sediment in the coastal zone.

Calibration of Businger-Arya Type of Eddy Viscosity Model's Parameters

Abstract: To solve the equation of motion for a turbulent oscillatory boundary layer, a suitable eddy viscosity model and its parameters are needed. The Businger-Arya type of eddy viscosity model, where the form of the eddy viscosity nearly linearly increases in the lower part of the boundary and exponentially decays in the outer part, has been recognized as one of the most suitable models. This model has three parameters to be determined. In this paper, these parameters are calibrated by comparison with a two-equation turbulence model.

Characteristics of Wave Reflection Spectra

Abstract: Experimental results of irregular wave reflection from impermeable walls and rubble mound breakwaters suggest that there is a characteristic form of wave reflection spectrum. The results indicate that the reflection coefficient at a particular frequency within a random wave spectrum is determined by an Iribarren number based on that frequency. An empirical relationship between reflection coefficient and local, frequency-dependent Iribarren number is provided for both structure types, although the range of parameters used in the rubble mound tests is limited. Therefore, the reflection coefficient spectrum can be determined from the structure slope, frequency, incident significant wave height, and two fitted coefficients that vary with structure type. Specification of the reflection coefficient spectrum becomes more critical as the width of the incident wave spectrum increases and as the Iribarren number decreases. Otherwise, random wave reflection can be adequately determined using the bulk reflection coefficient across the frequency range of the incident sea.

Estimating the Directional Spectrum of Waves Near a Reflector

Abstract: Near a reflector, incident waves are phase-locked to reflected waves and the wave field is spatially inhomogeneous, while far away from the reflector such phase-locking is unimportant. In this paper the theoretical and practical regions of validity of phase-locked (PL) and non-phase locked (non-PL) methods of directional wave analysis methods are investigated for both a collocated and a spatially separated configuration of instruments. A nondimensional framework is developed as a practical guide for the application of these methods in terms of \IL/S\N and \IT/S\N. Here \iL is the nondispersive time lag between the incident and reflected time series, \iS is the segment length of the fast Fourier transform, and \iT is the wave period. Numerical tests reveal that it is possible to use both methods with acceptable errors beyond their theoretical zones of validity. Equations are presented which predict regions of potential uncertainty and directional ambiguities in directional wave spectra. A numerical simulation method implemented in this contribution provides an effective means of testing the performance of different array geometries.