(PHD, 2000)

Abstract:

This study considers the run-up of non-breaking and breaking solitary waves on a smooth sloping beach. A non-linear theory and a numerical model solving the non-linear shallow water equations (NLSW) were developed to model this physical process. Various experiments to obtain wave amplitude time-histories, water particle velocities, wave free-surface profiles, and maximum run-up were conducted and the results were compared with the analytical and numerical models. A higher order theoretical solution to the non-linear shallow water equations, which describes the non-breaking wave characteristics on the beach, was sought and presented in this study. The solution was obtained analytically by using the Carrier and Greenspan (1958) hodograph transformation. It was found that the non-linear theory agreed well with experimental results. The maximum run-up predicted by the non-linear theory is larger than that predicted by Synolakis (1986) at the order of the offshore relative wave height for a given slope. This correction for non-breaking waves on beach decreases as the beach slope steepens, and increases as the relative incident solitary wave height increases. A unique run-up gage that consists of a laser and a photodiode camera was developed in connection with this study to measure the time-history of the tip of the run-up tongue of a non-breaking solitary wave as it progresses up the slope. The results obtained with this run-up gage agree well with other measurements and provides a simple and reliable way of measuring run-up time histories. The run-up of breaking solitary waves was studied experimentally and numerically since no fully theoretical approach is possible. The wave characteristics such as wave shape and shoaling characteristics, and, for plunging breakers, the shape of the jet produced are presented. The experimental results show that wave breaking is such a complicated process that even sophisticated numerical models cannot adequately model its details. Two different plunging wave breaking and resultant run-up were found from the experiments. The point, where the tip of the incident jet produced by the plunging breaking wave impinges determines the characteristics of the resulting splash-up. If the jet impinges on a dry slope, no splash-up occurs and the plunging breaker simply collapses. If the impingement point is located on the free-surface, splash-up including a reflected jet is formed, which further increases the turbulence and energy dissipation associated with wave breaking. It is hypothesized that both clockwise and counter clockwise vortices may be generated by the impinging plunging jet and the reflected jet associated with the splash-up when the jet impinges on the front face of a breaking wave or on the still water surface in front of the wave. If only the run-up process and maximum run-up are of interest, the wave and the water flow produced after breaking can be simplified as a propagating bore, which is analogous to a shock wave in gas dynamics. A numerical model using this bore structure to treat the process of wave breaking and propagation was developed. The non-linear shallow water equations were solved using the weighted essentially non-oscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and propagation is handled automatically 1w this scheme and no ad-hoc term is required. A computational domain mapping technique proposed by Zhang (1996) is used in the numerical scheme to model the shoreline movement. This numerical scheme is found to provide a somewhat simple and reasonably good prediction of various aspects of the run-up process. The numerical results agree well with the experiments corresponding to the run-up on a. relatively steep slope (1:2.08) as well as on a more gentle slope (1:19.85). A simple empirical estimate of maximum run-up based on energy conservation considerations is also presented where the energy dissipation associated with wave breaking was estimated using the results from the numerical model. This approach appears to be useful and the maximum run-up predicted agrees reasonably well with the experimental results. The splash-up of a solitary wave on a vertical wall positioned at different locations on a gentle slope was also investigated in this study to understand the degree of protection from tsunamis afforded by seawalls. It was found that the effect of breaking wave kinematics offshore of the vertical wall on the splash-up is of critical importance to the maximum splash-up. The maximum slope of the front face of the wave upon impingement of the wave on the wall, which represents the maximum water particle acceleration, was important in defining the maximum sheet splash-up as well as the trend for splash-up composed of drops and spray.

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(PHD, 1999)

Abstract:

Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used three-dimensional simulations of a bow wave to examine its air entrainment process. The simulated waves were created by a deflecting plate mounted at an angle in a super-critical free surface flow. Since the air entrainment process is closely coupled with breaking wave dynamics, the present study included both air entrainment and free surface measurements.

Measurements of the free surface wave were obtained from the simulated bow waves at two scales, and also from the bow wave created a towed wedge model. Contact line and bow wave profile measurements for the different experiments were compared, demonstrating the similarity of the experimental simulations to the towed model experiments. The plunging wave jet shape was measured in the larger scale stationary model and towed model experiments and used to calculate the jet thickness, velocity, and impingement angle. The bow wave profile data from the towed model experiments were used to investigate the scaling on the plunging wave face, and their wavelength, frequency, and velocity were measured.

The primary mechanisms for air entrainment were the impact of the plunging wave jet and individual droplets in the splash region on the free surface. The air entrainment process was observed in the larger scale stationary model experiments, and the air bubbles were entrained in spatially periodic bubble clouds. Due to the shallow depth in these experiments, measurements of only the larger bubbles in the initial stages of air entrainment were obtained. An impedance based void fraction meter, developed specifically for the purpose, was used to measure the void fractions and bubble size distributions beneath the wave. The bubble cloud size and void fraction increased with downstream distance.

There were indications that the surface disturbances control the periodicity of the bubble clouds. Namely, the surface disturbances divide the plunging liquid jet sheet into a series of plunging wave jets, each entraining air into a separate bubble cloud beneath the free surface.

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(PHD, 1997)

Abstract:

Water waves generated by underwater landslides threaten coastal communities near heads of fjords, near heads of underwater canyons, near river deltas, and on volcanic islands. This work provides a thorough analysis of water waves generated by two-dimensional underwater landslides using experimental, theoretical, and computational means. Water wave amplitudes generated by an underwater landslide are a function of the landslide length, the initial landslide submergence, the incline angle measured from horizontal, the characteristic distance of landslide motion, the characteristic duration of landslide motion, and the landslide rate of deformation. Nondimensional wavemaker curves constructed from the aforementioned parameters allow water wave amplitudes to be predicted. These wavemaker curves apply 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. Water wave amplitude predictions can be used for hazard mitigation studies.

An analytical solution of underwater landslide center of mass position in time provides the characteristic distance and time scales of landslide motion. Two-dimensional experimental results on a 45 degree incline confirm the existence of wavemaker curves for solid block landslides as a function of nondimensional geometrical quantities and what is called the Hammack number. The Hammack number is the correct nondimensional time for water wave generation problems. Water wave amplitudes generated by solid block landslides can be predicted from the wavemaker curves if the center of mass motion is known. The analytical solution reproduces the center of mass motion of solid block and granular material landslides. Experimental results of granular material landslides on a 45 degree incline show that landslide deformation reduces water wave amplitudes. Therefore, water waves generated by solid block landslides provide an upper bound on water waves generated by geometrically and kinematically similar deforming landslides. A criterion for the generation of linear water waves is given along with criteria for deep (or long) wave propagation down a constant depth channel. Simulations of water waves generated by underwater landslides were conducted with an inviscid fluid dynamics code. The waves simulated by the code agree reasonably well with experimental results.
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(PHD, 1993)

Abstract:

This study investigates the interaction of breaking waves with a bed of loose angular material with a median grain size of 4.8 mm. It is motivated by the engineering problem of determining rock sizes for revetments used as protection for structures in the coastal zone and by the need for an understanding of the mechanics of material movement under waves. Both the effect of the bed on the velocities and accelerations in breaking and non-breaking waves, and the effect of breaking waves on the movement of bed material is measured.

Velocities in breaking waves are measured at elevations approaching the bottom boundary, both for the case of a level bed of graded angular material and for a flat plate at the same location. By changing the water depth and the initial conditions of the incident wave, the relative size of the rock with respect to the breaking wave height is varied. Material movement resulting from the wave passage is measured and compared to the breaking wave height and to the turbulent shear determined near the bed. Using velocity and acceleration records near the rock bed together with observations of rock motion, the mechanics of material movement under waves are investigated.

The roughness elements in the bed are found to have a large effect on both the mean and fluctuating velocities in the wave near the bottom. Evidence is shown of the existence of an inner layer where individual pieces of bed material influence the flow over the bed. A method for determining the maximum mean shear under a single wave is presented. Mean vertical velocities are measured to be not negligible near the bed and are shown to produce convective accelerations of the same order as the accelerations due to turbulent fluctuations.

The movement of bed material is compared with the calculated shear on the bed and with local velocities and accelerations measured very close to the individual rocks. The mean size of the material moved in the bed is found to vary with the amount of shear on the bed. When adjusted for the mean size of the moved material, the calculated shears correspond well with the criterion for critical shear from the Shields curve used in steady flow. From the observed movement of particles during the passage of a wave and the measured velocities and accelerations in the wave, inertial forces are found to contribute to particle movement, especially in the regions before and after wave crest passage.
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(PHD, 1989)

Abstract:

The interaction of normally incident time-periodic water waves with a density-stratified fluid in a rectangular trench is studied experimentally and theoretically; the fluid outside the trench is homogeneous.

This investigation has focused on the excitation of internal waves in the trench by surface waves, and the effects of the internal oscillations on the waves on the free surface. The study shows that, when the frequency of the incoming surface waves corresponds to the natural frequency of oscillation of the internal waves in the trench, the amplitude of the internal waves becomes large compared to the amplitude of the surface waves. The effects of the internal waves on the surface waves were very small in the experiments.

A two-layer model and a three-layer model are developed and applied to a particular constant-depth channel and trench configuration used in the experiments. The two-layer model is also applied to a rectangular trench in an infinite region. These models treat steady-state wave motions of infinitesimal amplitude for all ranges of fluid depth relative to the wavelength of the surface waves, and include a vigorous treatment of the effects of energy dissipation in the laminar boundary layers adjacent to the solid surfaces and at the density interface. In the two-layer model the stratified fluid in the trench is represented by two homogeneous fluids of different densities; in the three-layer model these two fluids are separated in between by a transition region of linear density variation.

Fresh water and salt water were used to model density stratification in the experiments. The effects of surface wave amplitude and density distribution on the internal motion in the trench were investigated for small density differences compared to the density of water. A new technique using a scanning laser beam and detector system was developed to measure internal wave amplitudes. Satisfactory agreement with the theoretical predictions was obtained. The effects of nonlinearity and viscous dissipation on the internal motions were more pronounced when the depth of the heavier fluid was small compared to the wavelength of the internal waves in the trench.

For a trench in an infinite region, the two-layer model also predicts that large surface wave reflections occur when the trench is “at internal resonance,” and a significant portion of the incident wave energy can be dissipated within the trench.

The investigation has provided insight with regard to both the dynamics of wave-trench interaction and the design of navigation channels in density-stratified fluids for reducing the potential of wave-induced internal resonance.
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(PHD, 1986)

Abstract:

Wave breaking is investigated experimentally by use of laser doppler velocimetry for two cases: a plunging breaker and a spilling breaker. Specifically, emphasis is given to the kinematics at breaking, the early breaking phase, and the turbulent wake generated from wave breaking. A significant contribution is provided on the amplitude behavior for a solitary wave on a beach, as it is the solitary wave that is used to conduct this study. Associated with the use of the solitary wave, a technique of flow field construction by repeated measurement with an LDV is presented.

Four well defined regions of the shoaling-through-breaking solitary wave on a beach are identified and termed according to the wave amplitude behavior within each region. They are: the zone of gradual shoaling, the zone of rapid shoaling, the zone of rapid decay and the zone of gradual decay. The plunging wave case studied exhibited a definite transitional zone, between the previously known -1/4 and -1 power laws, following a power law of -3/5.

Velocity fields for a plunger and a spiller at the point of breaking are measured and the corresponding acceleration fields are computed for each. The results show good qualitative comparison to those obtained by theoretical approaches, however, no clear mechanism is demonstrated to initiate breaking for the spilling breaker studied.

The existence of counter-rotating vortices, generated from breaking, is established from velocity measurements of the flow taken during the early breaking phase and within the turbulent wake of the plunging breaker studied. The measurements indicate that the size of the vortices are roughly the same as the undisturbed depth at the point of breaking. Turbulent intensities determined within the wake of the plunging breaker illustrate its character and show that level of turbulent intensity does not progressively decrease behind the turbulent source.

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(PHD, 1986)

Abstract:

This is a study of the fundamental physical processes of the runup of long waves with the objective to understand some coastal effects of tsunamis.

The runup of nonbreaking long waves on plane beaches is studied and an exact solution is developed for the runup of solitary waves. The maximum runup predicted by this solution is compared to laboratory data from this and other investigations and it is found to be in good agreement. A runup transducer was developed and deployed in the laboratory to provide data for the shape of the runup tongue. The exact solution is shown to model the details of the climb of the wave satisfactorily.

The runup of breaking long waves on plane beaches is investigated in the laboratory by studying different long waves and bores of finite volume. The runup is shown to be a function of a momentum scale determined from the generation characteristics of the incoming wave. The runup number is introduced and it is demonstrated that it models the runup process adequately. It is also observed that arbitrary long waves have runup numbers smaller than, or at most equal to, the runup number of breaking solitary waves, suggesting that on a given plane beach breaking solitary waves run-up further than other long waves with similar generation characteristics.

An exact result is established for the force on an accelerating plate in a fluid with a free surface. The result is used to explain some of the results of this study and other results on the hydrodynamic forces on moving partitions.

A technique is developed to generate arbitrary, long, continuously evolving waves at any desired location in a laboratory model. The technique is applied in the laboratory and it is shown to be successful in reproducing complex waveforms.

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(PHD, 1986)

Abstract:

The influence of sloping boundaries on the long wave response of bays and harbours is studied in this work. Laboratory experiments are performed to help validate the theoretical analysis which is applicable to nonbreaking waves.

A set of long wave equations in the Lagrangian description is derived which includes terms to account for nonlinear, dispersive, and dissipative processes for wave propagation in two horizontal coordinates. A finite element model is developed based on these equations which is capable of treating arbitrary geometry and the runup of nonbreaking waves on a beach.

An analytical harbour response model, capable of treating narrow rectangular harbours with variable bathymetry and sidewall geometry, is developed and applied to several simple geometries. The model shows that for a given harbour length and entrance width, the resonant frequencies and the response of a harbour are very dependent on the harbour sidewall geometry and bathymetry.

Some of the nonlinear effects of the runup of nonbreaking periodic waves on a plane beach are discussed. In particular, the time average of the water surface time history at a fixed spatial location is negative and the wave crests are smaller than the troughs. Nonlinear effects do not alter the runup maxima or minima and the maximum fluid acceleration occurs at the point of maximum rundown of the wave.

Laboratory experiments were performed to determine the long wave reponse of a narrow rectangular harbour whose still water depth decreases linearly between the harbour entrance and the shoreline. Good agreement with the finite element model was obtained, including the prediction of the depression of the mean water level within the harbour.

A three-dimensional application of the finite element model treats the runup of solitary waves on a coastline with variable bottom topography and a curved shoreline. The results indicate that the model can predict the trapping of wave energy along a sloping coastal margin, a process of fundamental importance for predicting potential tsunami damage.

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(PHD, 1981)

Abstract:

The process of excitation of harbors and bays by transient nonlinear long waves is investigated theoretically and experimentally. In addition, nonlinear shallow water waves generated in a closed rectangular basin by the motion of the basin are also examined.

Two numerical methods based on finite element techniques are used to solve the weakly nonlinear-dispersive-dissipative equations of motion and are applied to the basin excitation problem and the transient harbor oscillation problem, respectively. In the latter case, the open sea conditions are simulated by including a radiative boundary condition in time at a finite distance from the harbor entrance. Various dissipative effects are also included. In addition to the numerical results, analytical solutions are presented to investigate certain particular aspects of basin and harbor oscillations (e.g., the effects of viscous dissipation in a harbor with simple geometry).

Experiments conducted in the closed rectangular basin indicate that for a continuous excitation at or near a resonant mode of oscillation the linear theory becomes inadequate and the nonlinear-dispersive-dissipative theory must be used. For a transient excitation the validity of the linear theory depends on the value of the Stokes parameter. Indeed, some features not predicted by the linear theory can be directly inferred from the magnitude of this parameter.

Experiments on the continuous wave induced oscillations of a narrow rectangular harbor with constant depth show that at the first resonant mode convective nonlinearities can be neglected and a linear dissipative solution is sufficient to describe the waves inside the harbor. At the second resonant mode which corresponds to a longer harbor relative to the length of the incident wave, nonlinear convective effects become important and must be incorporated into the numerical model. Also the characteristics of various sources of dissipation which reduce resonance in the harbor are investigated experimentally. The sources considered include, among others, laminar boundary friction, leakage losses underneath the harbor walls, and energy dissipation due to flow separation at the entrance of the harbor.

The good agreement obtained between the experiments and the nonlinear numerical model developed in this study suggests that this model could be used with some confidence to predict the response characteristics of prototype harbors. As an example, the results of this study have been applied to the response of Ofunato Bay (Japan) to the tsunami generated by the Tokachi-Oki earthquake of May 16,1968. The model has been used to investigate the effects of convective nonlinearities on the bay oscillations and also to determine the efficiency of the breakwater which was built to reduce the effects of tsunamis at Ofunato.

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(PHD, 1979)

Abstract:

The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf.

A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments.

A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories.

The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented.

Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

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(PHD, 1976)

Abstract:

An empirical relationship is presented for the incipient motion of bottom material under solitary waves. Two special cases of bottom material are considered: particles of arbitrary shape, and isolated sphere resting on top of a bed of tightly packed spheres.

The amount of motion in the bed of particles of arbitrary shape is shown to depend on a dimensionless shear stress, similar to the Shields parameter. The mean resistance coefficient used in estimating this parameter is derived from considerations of energy dissipation, and is obtained from measurements of the attenuation of waves along a channel. A theoretical expression for the mean resistance coefficient is developed for the case of laminar flow from the linearized boundary layer equations and is verified by experiments.

For the case of a single sphere resting on top of a bed of spheres, the analysis is based on the hypothesis that at incipient motion the hydrodynamic moments which tend to remove the sphere are equal to the restoring moment due to gravity which tends to keep it in its place. It is shown that the estimation of the hydrodynamic forces, based on an approach similar to the so-called “Morison’s formula”, in which the drag, lift, and inertia coefficients are independent of each other, is inaccurate. Alternatively, a single coefficient incorporating both drag, inertia, and lift effects is employed. Approximate values of this coefficient are described by an empirical relationship which is obtained from the experimental results.

A review of existing theories of the solitary wave is presented and an experimental study is conducted in order to determine which theory should be used in the theoretical analysis of the incipient motion of bottom material.

Experiments were conducted in the laboratory in order to determine the mean resistance coefficient of the bottom under solitary waves, and in order to obtain a relationship defining the incipient motion of bottom material. All the experiments were conducted in a wave tank 40 m long, 110 cm wide with water depths varying from 7 cm to 42 cm. The mean resistance coefficient was obtained from measurements of the attenuation of waves along an 18 m section of the wave tank. Experiments were conducted with a smooth bottom and with the bottom roughened with a layer of rock. The incipient motion of particles of arbitrary shape was studied by measuring the amount of motion in a 91 cm x 50 cm section covered with a 15.9 mm thick layer of material. The materials used had different densities and mean diameters. The incipient motion of spheres was observed for spheres of different diameters and densities placed on a bed of tightly packed spheres. The experiments were conducted with various water depths, and with wave height-to-water depth ratios varying from small values up to that for breaking of the wave.

It was found that: (a) The theories of Boussinesq (1872) and McCowan (1891) describe the solitary wave fairly accurately. However, the differences between these theories are large when used to predict the forces which are exerted on objects on the bottom, and it was not established which theory describes these forces better. (b) The mean resistance coefficient for a rough turbulent flow under solitary waves can be described as a function of D_{s}, h, and H, where D_{s} is the mean diameter of the roughness particles, h is the water depth, and H is the wave height. (c) Small errors in the determination of the dimensionless shear stress for incipient motion of rocks result in large errors in the evaluation of the diameter of the rock required for incipient motion. However, it was found that the empirical relationship for the incipient motion of spheres can be used to determine the size of rock of arbitrary shape for incipient motion under a given wave, provided the angle of friction of the rock can be determined accurately.

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(PHD, 1972)

Abstract:

A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered.

An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model.

Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of non-linear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation.

A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation.

An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally.

The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.

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(PHD, 1970)

Abstract:

Theoretical and experimental studies were conducted to investigate the wave induced oscillations in an arbitrary shaped harbor with constant depth which is connected to the open-sea.

A theory termed the “arbitrary shaped harbor” theory is developed. The solution of the Helmholtz equation, ∇^{2}f + k^{2}f = 0, is formulated as an integral equation; an approximate method is employed to solve the integral equation by converting it to a matrix equation. The final solution is obtained by equating, at the harbor entrance, the wave amplitude and its normal derivative obtained from the solutions for the regions outside and inside the harbor.

Two special theories called the circular harbor theory and the rectangular harbor theory are also developed. The coordinates inside a circular and a rectangular harbor are separable; therefore, the solution for the region inside these harbors is obtained by the method of separation of variables. For the solution in the open-sea region, the same method is used as that employed for the arbitrary shaped harbor theory. The final solution is also obtained by a matching procedure similar to that used for the arbitrary shaped harbor theory. These two special theories provide a useful analytical check on the arbitrary shaped harbor theory.

Experiments were conducted to verify the theories in a wave basin 15 ft wide by 31 ft long with an effective system of wave energy dissipators mounted along the boundary to simulate the open-sea condition.

Four harbors were investigated theoretically and experimentally: circular harbors with a 10° opening and a 60° opening, a rectangular harbor, and a model of the East and West Basins of Long Beach Harbor located in Long Beach, California.

Theoretical solutions for these four harbors using the arbitrary shaped harbor theory were obtained. In addition, the theoretical solutions for the circular harbors and the rectangular harbor using the two special theories were also obtained. In each case, the theories have proven to agree well with the experimental data.

It is found that: (1) the resonant frequencies for a specific harbor are predicted correctly by the theory, although the amplification factors at resonance are somewhat larger than those found experimentally,(2) for the circular harbors, as the width of the harbor entrance increases, the amplification at resonance decreases, but the wave number bandwidth at resonance increases, (3) each peak in the curve of entrance velocity vs incident wave period corresponds to a distinct mode of resonant oscillation inside the harbor, thus the velocity at the harbor entrance appears to be a good indicator for resonance in harbors of complicated shape, (4) the results show that the present theory can be applied with confidence to prototype harbors with relatively uniform depth and reflective interior boundaries.

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(PHD, 1970)

Abstract:

The major objective of the study has been to investigate in detail the rapidly-varying peak uplift pressure and the slowly-varying positive and negative uplift pressures that are known to be exerted by waves against the underside of a horizontal pier or platform located above the still water level, but not higher than the crests of the incident waves.

In a “two-dimensional” laboratory study conducted in a 100-ft long by 15-in.-wide by 2-ft-deep wave tank with a horizontal smooth bottom, individually generated solitary waves struck a rigid, fixed, horizontal platform extending the width of the tank. Pressure transducers were mounted flush with the smooth soffit, or underside, of the platform. The location of the transducers could be varied.

The problem of a d equate dynamic and spatial response of the transducers was investigated in detail. It was found that unless the radius of the sensitive area of a pressure transducer is smaller than about one-third of the characteristic width of the pressure distribution, the peak pressure and the rise-time will not be recorded accurately. A procedure was devised to correct peak pressures and rise-times for this transducer defect.

The hydrodynamics of the flow beneath the platform are described qualitatively by a si1nple analysis, which relates peak pressure and positive slowly-varying pressure to the celerity of the wave front propagating beneath the platform, and relates negative slowly-varying pressure to the process by which fluid recedes from the platform after the wave has passed. As the wave front propagates beneath the platform, its celerity increases to a maximum, then decreases. The peak pressure similarly increases with distance from the seaward edge of the platform, then decreases.

Measured peak pressure head, always found to be less than five times the incident wave height above still water level, is an order of magnitude less than reported shock pressures due to waves breaking against vertical walls; the product of peak pressure and rise-time, considered as peak impulse, is of the order of 20% of reported shock impulse due to waves breaking against vertical walls. The maximum measured slowly-varying uplift pressure head is approximately equal to the incident wave height less the soffit clearance above still water level. The normalized magnitude and duration of negative pressure appears to depend principally on the ratio of soffit clearance to still water depth and on the ratio of platform length to still water depth.

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(PHD, 1966)

Abstract:

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream.

Taylor’s method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required.

Large values of the dimensionless dispersion coefficient D/rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio.

A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments.

Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington.

Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factory of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor’s analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.

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