Within this master thesis the behaviour of long periodic waves during their run-up on a plain beach was investigated via physical and numerical modelling. In the experimental part, for seven leading depression, non-breaking sine waves with surf similarity parameters between 3.1 and 15.6 the wave velocity, wave height and run-up on a plain beach were determined. In addition, the motion of the initially still shoreline, i.e. run-up/ run-down process, run-up/ run-down velocity, wave acceleration, maximum run-up and maximum run-up velocity, was determined via two high-speed cameras. Comparison of the aforementioned characteristics with the theory revealed good agreement; deviations can mostly be attributed to experimental performance.
For wave generation a new volume driven wave generator was used. Long waves are generated by a pair of high capacity pumps under control of a proportional-integral-derivative controller (PID-controller). While rotating clockwise or counterclockwise water is pumped into the propagation section or extracted from it. Thereby, waves of arbitrary length can be generated.
Using the relatively new strategy of observing the shoreline motion via optical measurements gave a comparatively exact shoreline position during wave run-up. In contrast, determination of the shoreline position during run-down was less exact due to missing evidence indicating the distinct position of the shoreline. In general, the experimentally determined shoreline position agreed with the theoretical approach. The maximum run-up/ run-down occurred for waves with surf similarity parameters between 3 and 6 (interval in which transition from breaking to non-breaking occurs). The magnitude of the theoretical breaking point increased for decreasing wave non-linearity A/h. For surf similarity parameters greater equal of the theoretical breaking point and for increasing surf similarity parameters the normalized run-up and magnitude of normalized run-down decreased. The maximum run-up/ run-down was proportional to wave non-linearity, i.e. the normalized run-up and magnitude of normalized run-down decreased with increasing wave amplitude as predicted by theory. The agreement of experimental and theoretical maximum run-down/ run-up depended on tuning of the PID controller and the resulting actual curve. For longer waves suboptimal tuning of the PID controller resulted in riding waves.
Contents
1 Introduction
1.1 Motivation
1.2 General Information on Tsunamis
1.3 Scope of the Thesis
1.4 Outline of the Thesis
2 Literature Review
2.1 Long Wave Generation Techniques
2.1.1 Piston-type Wave Generation
2.1.2 Dam Break Analogy
2.1.3 Vertical Sea Bed Motion
2.1.4 Pneumatic Wave Generation
2.2 The Brier Score
2.3 The Shoreline Motion of Long Sinusoidal Waves
2.4 Breaking Criterion for Sinusoidal Waves
2.5 Optical Measurements of Long Wave Run-up
3 Experimental Setup
3.1 Description of Instruments
3.1.1 The Wave Flume
3.1.2 The Wave Gauges
3.1.3 The Velocity Meter
3.1.4 The Pressure Sensors
3.1.5 The High Speed Cameras
3.2 Performance of Physical Experiments
3.3 Data Processing
3.3.1 Processing of Time Series
3.3.2 Image Processing
3.3.3 Derived Quantities: Position, Velocity and Acceleration of the Shoreline
4 Wave Generation
4.1 Introduction
4.2 The Pump-driven Wave Generator
4.3 The Controller Scheme
4.4 Summary
5 Results Of Physical Experiments
5.1 Time Series
5.1.1 Comparison Reference and Actual Curve, Brier Score
5.1.2 Time Series of Wave Gauges
5.1.3 Time Series of EMS Sensor
5.1.4 Time Series of Pressure Sensors
5.2 Run-up and Run-down of Long Waves
5.3 Maximum Run-up and Run-down
5.4 Shoreline Velocity During Run-up and Run-down
5.5 Maximum Shoreline Velocity During Run-up and Run-down
5.6 Wave Acceleration During Run-up and Run-down
5.7 Summary
6 Numerical Model Test
6.1 Introduction
6.2 Description of the Numerical Model
6.3 Results of the Numerical Model Study
6.3.1 Evolution of SSH During Propagation
6.3.2 Numerical Shoreline Location and Maximum Run-Up
6.4 Summary
7 Summary and Outlook
Research Objectives and Key Topics
This master thesis investigates the behavior of long periodic waves during their run-up on a plain beach using both physical and numerical modeling techniques. The primary research objective is to analyze the correlation between wave characteristics (such as wave length, period, and amplitude) and the resulting shoreline motion, including run-up/run-down processes and velocities, while validating a 2D shallow water numerical model against experimental data.
- Physical modeling of long, non-breaking sine waves in a specialized wave flume.
- Advanced optical measurement strategies for tracking shoreline motion.
- Development and validation of a numerical shallow water model (TAM).
- Analysis of shoreline velocity, acceleration, and maximum run-up/run-down heights.
- Assessment of the PID controller performance for wave generation.
Excerpt from the Book
1.1 Motivation
On December 26, 2004 at 01:01:09 UTC a submarine earthquake of magnitude M = 9.0 hit the western coast of northern Sumatra, Indonesia (Wang & Liu, 2006). The main shock had its epicenter at 3.09°N and 94.26°E, i.e. on a fault line extending from Indonesia northward to the Andaman Islands. Here, the Indo - Australian plate subducts beneath Sunda plate and Burma sub-plates at a celerity of approximately 60 mm/year in northeastern direction (Wang & Liu, 2006). Along the fault line and on a section extending 1200 km to 1300 km northward from the epicenter the seafloor was uplifted by up to 10 m. As a consequence of the earthquake several tsunami waves were generated that spread at a velocity of approximately 700 km/h radial from the epicenter. The first wave arrived at Sri Lanka two hours after the main shock. Three hours after the shock the waves arrived at the Maldives. Along the Indonesian coast wave heights of up to 30 m were observed. In Phuket, Thailand wave heights of 10 m were reported (Wang & Liu, 2006). In total, 283, 100 people lost their life and 14, 100 people are still missing. In 10 countries located around the Indian Ocean 1, 126, 900 people lost their home. The tsunami waves even crossed the southern Atlantic Ocean to arrive at the east coast of Africa where they caused enormous material damage and killed many people (Wang & Liu, 2006).
Summary of Chapters
1 Introduction: Provides the background motivation regarding tsunami research and outlines the primary goal of studying shoreline motion using physical and numerical models.
2 Literature Review: Reviews existing techniques for long wave generation, the use of the Brier Score, and established theoretical frameworks for shoreline motion.
3 Experimental Setup: Details the design of the wave flume, measurement instruments, and the methodology used for data acquisition and processing.
4 Wave Generation: Describes the innovative pump-driven wave generator and the proportional-integral-derivative (PID) controller scheme.
5 Results Of Physical Experiments: Analyzes the gathered experimental data, comparing shoreline motion and velocities against theoretical predictions.
6 Numerical Model Test: Covers the application and validation of the 2D shallow water model TAM using the experimental dataset.
7 Summary and Outlook: Synthesizes the overall findings and provides recommendations for future research directions.
Key Words
Tsunami, Run-up, Run-down, Shoreline Motion, Physical Modeling, Numerical Modeling, Wave Flume, PID Controller, Shallow Water Equations, Brier Score, Surface Elevation, Wave Generation, Finite Element Model, Surf Similarity, Inundation
Frequently Asked Questions
What is the primary focus of this thesis?
This thesis examines the run-up and run-down behavior of long, non-breaking periodic waves on a plain, uniformly sloping beach through experimental laboratory tests and numerical validation.
What are the central thematic fields?
The core topics include physical wave generation, optical measurement techniques for shoreline tracking, fluid dynamics during wave run-up, and the validation of finite element numerical models.
What is the main research objective?
The objective is to fill the data gap regarding shoreline motion (velocity and location) during long-wave run-up/run-down and to assess the reliability of a 2D shallow water numerical model.
Which scientific methods are utilized?
The work employs physical modeling in a controlled wave flume environment, high-speed camera image processing for shoreline detection, and a 2D shallow water finite element model named TAM.
What is covered in the main section of the work?
The main part documents the design of the physical experiments, the specific wave generation techniques used, the analysis of gathered sensor and camera data, and the subsequent numerical simulation tests.
What are the key descriptors for this work?
Important keywords include Tsunami, Run-up, Shoreline Motion, Physical Modeling, Numerical Modeling, Wave Flume, and PID Controller.
How were the waves generated in the laboratory?
A specialized volume-driven wave generator using four high-capacity pipe pumps under a PID controller feedback loop was used to generate waves of arbitrary length.
Why was an optical measurement strategy used?
Optical measurement using high-speed cameras provides a relatively new and highly resolved method for tracking the dynamic shoreline position on a beach, which is difficult to measure with traditional point sensors.
What were the main findings regarding the numerical model?
While the model performed well on the wet part of the beach, it struggled with the complex flooding/inundation process on initially dry cells and needs further algorithmic refinement.
- Quote paper
- Ulrike Drähne (Author), 2014, Experimental and numerical determination of the shoreline motion during the run-up of tsunami waves on a plain beach, Munich, GRIN Verlag, https://www.grin.com/document/280860
