This study deals with the impingement of a non-breaking and a breaking solitary wave:.; on a smooth sloping beach. This approach appears to be useful and the predicted peak momentum agrees reasonably well with the experimental results.
List of Figures
1G7 5.41 Energy Dissipation in the Onset of a Breaking Solitary Wave: A Comparison . between the numerical results and the empirical formula Eq. 5.41 1G8 5.42 Definitional sketch of the energy balance model for resting in solitude . wave rUll-Up. Sketch of experimental set-up used to measure wave reflection 179 5.47 l\laximal height of reflected wave to break i-lolite wave run-up after .. elimination of run-up tongue as a function of relative height of incident wave .. function of relative incidcllt waw height.
List of Tables
Nomenclature
Chapter 1 Introduction
- Tsunamis
- Objective and Scope
- Thesis Outline
In fact, most of the damage associated with tsunamis is related to their run-up at the coastline. A numerical method for solving the nonlinear shallow water wave equations and a special treatment of the wave breaking process and the moving shoreline are also described.
Chapter 2 Literature Review
- Theoretical Analyses
- Laboratory Experiments
- Numerical Simulations
The maximum run-up was found to be largest in front of the island (facing the direction of wave attack). ZeIt (1991a) applied this model to the case of both unbreakable and breaking wave run-up on a flat shore.
Chapter 3 Theoretical Analysis
- Non-Breaking Solitary Wave Run-Up
- Governing Equations and Basic Assumptions
- Theoretical Considerations - Existing Theories
- Theoretical Considerations - The Non-Linear Theory
- Numerical Simulation of Breaking Solitary Wave Run-Up - WENO Scheme
- Mathematical Formulation
- Numerical Model and Treatment of a Moving Shoreline
- Weighted Essentially Non-Oscillatory (WENO) Shock- Capturing Scheme
- Boundary Conditions
- Test Cases
We are now unable to compare the solitary wave flow predicted by the approximate nonlinear theory and the current nonlinear theory. where, as before, s is the speed of the tip of the shoreline, i.e., the tip of the attached tongue. It is noted that in Eq. 3.51 the first integral is identical to Eq. 3.23, i.e., the maximum advance predicted by the linear theory and the approximate nonlinear theory.).
Chapter 4 Procedures
- Wave Tanks and Wave Generation System
- Wave Tanks
- Wave Generation System
Stainless steel rails 3.1)1 em in diameter are molded along the top edge of the wave tank and are leveled to within ±O.3 mm. ),Iovable instrument carriages are designed for these rails. An aluminum ramp is installed on one side of the web which is connected to the constant depth area with the toe of slope 17.30 m from the wave generator. After that, the inclination of the frame module was adjusted to the desired angle by changing the four leveling screws on both sides.
A sketch is shown in Figure 4.5 showing the wave tank and the setup of the experiments. A small wedge made of lucitec was machined and installed on top of the slope to eliminate the gap between the bottom of the wave tank and the beach. The beach was installed with the top of the slope 12.35 m from the wave generator and the slope of the beach was also adjustable; for these experiments it was set at 1:2.08 with a deviation from a flat surface of less than ±1 lIUll.
A photograph of the experimental setnp of solitary wave flow without discontinuity is shown in Figure 4.G.
Return
Supply Servo controller
Trajectory Generation
The desired trajectory of the wave generator was provided to the servo controller as a time series of discrete voltage levels. The signal was then transferred from tIl(' computer to the servo controller by means of a D/A converter with buffer storage (manufactured by Shapiro Scientific Instruments (SSI), Corona del l\Iar. CA). An amplifier which was also designed by SSI was used to adjust the gain of the generated signal so that a large range of the movements can be realized.
The wave paddle home position can also be adjusted by adding or subtracting an offset voltage from the signal sent to the servo valve. The relationship between the gain setting and the desired wave paddle stroke was determined and the resulting calibration curve was used in the experiments. Figure 4.10 shows an example trajectory output from the personal computer for generating solitary waves.
Water Surface Elevation Measurements
- Resistance Wave Gage
- Capacitance Wave Gage
As the water level changes. the voltage imbalance caused by the changed resistance of the meter is monitored and amplified by a preamplifier. The depth of immersion of the wavemeter was changed in increments of 0.5 em while the voltage output of the electronics was recorded. In Figure 5.2 of Chapter 5, a comparison of the wave amplitude obtained from resistance wave meters and that of a high-speed video recording will be presented.
This comparison showed that the drag wavemeter appears to have an adequate dynamic response to resolve the time-varying water surface of the solitary wave used in this study. The error in varying the position of the wavemeter and the error caused by the approach of the meter to the tank bottom is also discussed by Ramsden (1993). A photograph of the capacitance wavemeter used is shown in Figure 4.13 and discussed by Synolakis (1987).
Because the distance of the probe to the surface of the slope was always the same.
Run-Up Gage
Synolakis (1986) attributes the difference to the difficulty in identifying the free-surface location in the film frames because the windows of the tank were wet during the run-up. The electrical output signal from the camera was a composite video signal that included a time pulse and an analog signal that represented the gray scales of the line measured along the slope. Because the intensity of the laser spot on the slope was much greater than the ambient light, a pulse-like signal showed the location of the laser spot.
This train of pulses was then integrated to produce an analog voltage output whose amplitude is directly proportional to the duty cycle time. The run-in meter was calibrated by reflecting a laser into a camera at known positions along the slope. There are some limitations to the use of this instrument during the discharge procedure.
Chapter 5 presents and discusses the comparison of the Roll-Up tongue measurement with this particular roll-up meter and high-speed video.
Water Particle Velocity Measurement
Once the wave broke, air bubbles entrained in the breaking region obscured the laser beam and velocity data could not be obtained. The data acquisition mode of the LDV system was set to random, which meant that the horizontal velocity signal and vertical velocity signal could be acquired independently during the experiments. The horizontal coordinates of the laser beam could be accurately determined within 0.1 mm by a scale attached to the platform.
The vertical position of the laser beam was determined by a spot meter on the wave tank. Vater particle veiocitiefi was obtained at several locations ranging from the tone of the filope to lokatiollfi ncar the initial fihoreline. A wavemeter (capacitance wavemeter or resistance wavemeter. depending on the local water depth of tlw measuring point) was placed in the wave tank above the laser beams to simultaneously measure the height of the water surface.
If the local water depth was not deep enough to allow both the wavemeter and the laser beams to be at the same position.
High-Speed Video Equipment
- Sideview Recording
- Over head Recording
A vertical pole was connected to the carriage on the other side of the surge tank to carry light (see Figure 4.21). A translucent panel was placed on the other side of the wave tank to provide a uniformly illuminated background and to prevent direct light from the camera. Each mark was made of black tape and stuck to the outer glass wall of the wave tank.
The camera was mounted on a swivel mount attached to the inner frame of the cart discussed in the previous section. A photograph of a high SI)('cd camera in an overhead position is shown in Fig. 4.23. Distortion is quite pronounced if the camera axis is not perpendicular to the side walls of the wave tank or if the field of view is too large.
Due to the difficulty in accurately positioning the camera and the need to increase the area covered.
Vertical Wall
All points except the rectangle in the image were calibrated with corner coordinates, and the distortion was caused by the camera optics.
Data Acquisition System
Experimental Procedures
- Measurements of the Run-Up of Solitary Waves on Slopes
- Measurements of the Splash-Up of Solitary Waves on Vertical Walls
- Other Experimental Procedures
The time histories of the rise of solitary waves on the slopes were measured by two methods: (i) the surge meter presented in the previous section. Time histories of the falling process could not be recorded by the high-speed vid camera (~o) because the slope surface was already wetted by the rUll-Up wave; therefore, the reversal current cannot be recognized in the images. The peak solitary wave growth on the slope was also measured by two methods: (i) high-speed video recording and (ii) visual observations plus point gauge.
Then, the height of the mark relative to the original shoreline was measured using a point measure. The experimental set-up was the same as for the run-up experiments on a slope, except that a vertical wall was mounted on the slope. However, when the wave broke near the position of the vertical wall, the spray was quite high and broke up with the drops and spray.
A second high-speed video camera was placed on one side of the wave tank to record the wave breaking shape from a side view.
Chapter 5 Presentation and Discussion of Results
- Solitary Wave Characteristics
- Non-Breaking Solitary Wave Run-up
- Wave Amplitude and Velocity Time-Histories
- Free Surface Profiles
- Shoreline Movement and Maximum Run-Up
- Energy Transformation in the Run-Up Process
- Breaking Solitary Wave Run-Up
- Wave Breaking Characteristics
- Breaking Solitary Wave Run-Up - Comparison with Results from the WENO Scheme
- Breaking Solitary Wave Run-Up - An Exploration of Energy Conservation
In the region near the upwelling maxima (Figure 5.7 (e), t* = 10.2), the current theory tends to overestimate the amplitude of the upwelling tongue compared to experiment. Adding the potential energy and the kinetic energy together. the total energy of the wave can be obtained. The solid line is the experimental results. the dashed line is the numerical results from Grilli et a1. one is the thickness of the beam in the vertical plane of the wave.
The length of the beam relative to the distance between the location where the wave crest breaks, i.e. the acute angle of the water surface obtained in the numerical results shown in Figure 5.30(k) and (1) is not realistic. The time Tc is defined as the end of wave breaking for the ramp-up process.).
Runup Process
