TSUNAMI WAVE BREAKING BEHAVIOR ON A REEF WITH A ...

TSUNAMI WAVE BREAKING BEHAVIOR ON A REEF WITH A ROUGH SURFACE
Kimberly J. Quesnel
California Polytechnic State University, San Luis Obispo
REU Institution: Oregon State University
Principle Investigators: Dr. Ian Robertson, Dr. Ronald Riggs, Dr. Kwok Fai Cheung
Graduate Student Advisor: Pablo Duarte Quiroga

1. Abstract
This study is part of the University of Hawaii at Manoa’s HIREEF 2 project and aims to analyze the
breaking behavior of tsunami waves over a reef shape similar to the ones present on tropical islands like
Hawaii. In addition, energy dissipation due to bottom roughness was investigated and proven to be
significant. When roughness was in the zone before breaking, waves were smaller, broke sooner, and
crashed sooner than waves that propagated over roughness which had been placed after breaking.
When looking at breaking characteristics in comparison to previous research where only a mild slope
was considered, the waves in this experiment had a higher breaking index (wave height at
breaking/water depth at breaking) and a lower water depth at breaking due to the geometry of the
bottom surface, indicating that bathymetry plays a role in wave breaking. In the future, better
understanding of the breaking behavior and energy dissipation of tsunami waves due to roughness and
reef geometry will lead to more accurate numerical models that can then be used as engineering tools
to save both infrastructure and lives in tsunami hazard zones.
2. Introduction and Literature Review
Tsunamis occur when underwater earthquakes, landslides, or volcanic eruptions create massive
displacements of water that travel towards the shore at alarming speeds. When these massive waves
reach the coastline, they are capable of causing enormous damage to infrastructure and killing
thousands of people. It is crucial that we study tsunami events and wave propagation not only to
improve our understanding of the phenomena, but so we can create improved building codes that can
lead to enhancing human safety and improving our coastal management. The HIREEF 2 project is aimed
at studying how tsunamis and structures are affected by bathymetry specific to the Hawaiian region and
other islands. This particular part of the HIREEF project works to understand the effect of roughness and
reef geometry on the breaking of these waves. By observing the wave breaking characteristics, the wave
energy dissipation due to roughness and geometry can be estimated.
Tsunamis are characterized by long wave lengths, and can
therefore be simply modeled as solitary waves with
theoretically infinite wavelengths (Young et al 2008). The
hydrodynamic similarities between these two types of
waves have been proven and solitary waves are therefore
used in most experiments relating to tsunamis, including
this one. This experiment differs from previously
completed studies by Grilli et al. (1997) in that roughness is
introduced by using timber planks installed in the bottom of
the wave flume, as well as island reef bathymetry as seen by
the steep slope and flat reef configuration of the tank.
Figure 1: Bathymetry of the Hawaiian Islands.
(SOEST, 2009)
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3. Methods
3.1 Facility
This experiment was carried out at the O.H. Hinsdale Wave Research Laboratory at Oregon State
University in the Two-Dimensional Wave Flume (Figure 2). The tank measures 104m long by 3.7m wide
by 4.6m deep, and a large stroke piston-type wavemaker is used to generate long wave tsunamis. The
bottom of the flume is movable and therefore able to be configured in many different ways by placing
concrete slabs at various depths and slopes along the tank. With the wavemaker as the datum (x=0), the
bathymetry for this experiment was configured such that
the first 28.6m was flat, the middle 25.6m was sloped
upwards and the last 35.8m was again flat. The slope of the
middle section remained at a constant 1:12 ratio
throughout the entire duration of the HIREEF 2 project. This
slope was considered to be steep as necessitated by the
characteristics of a reef shape. Since tsunamis and reefs
alike have a drastic range of sizes, it would be unreasonable
to try to quantitatively scale the experiment in comparison
to the real world. Therefore the project was not aimed at
mimicking a particular tsunami at a specific location.
Figure 2: Wave flume at the O.H. Hinsdale Wave
Research Laboratory at Oregon State University.
Figure 3: Diagram of wave flume and wave variables: water depth from tank bottom (ho), wave height from free surface
(Ho), wave depth at breaking (hb), wave height at breaking from free surface (Hb), distance of breaking (db), distance of
crashing (dc). The wavemaker location is represented by x=0.
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3.2 Instrumentation
Instruments were used for this particular aspect of the project to
determine the free surface profile of the water as a wave passed. Fourteen
resistance-type parallel wire wave gauges and eight sonic wave gauges
(Figure 4) recorded the height of the waves over time and were positioned
down the length of the tank in the horizontal x-direction. The
measurements from these instruments were used to record the actual
wave height Ho and compare the values to the experimental Ho, the
number that was entered into the wavemaker computer. The actual wave
height values were typically 3-5% lower than the wave height input in the
computer, and therefore the difference was not taken into account in this
analysis.
Figure 4: Wave measurement
instrumentation: sonic wave
gauge (left) and wire wave
gauge (right)
3.3 Wave Trials
In order to gather a broad spectrum of data, waves were run at combinations of 9 different wave height
ratios and 5 different water depths (0cm, 5cm, 10cm, 20cm, and 30cm above the flat reef). Trials of
wave height ratios equal to 0.1, 0.2, 0.3, 0.4, and 0.5 were run twice in order to test repeatability. By
combining these variables in different ways, different aspects affecting the waves could be isolated.
Waves were run every 20-30 minutes in order to allow the water to settle.
3.4 Breaking Index and Breaker Type
There are four ways in which breaking waves can be classified. These “breaker types” are spilling,
plunging, collapsing, and surging. Spilling waves are characterized by a crest that becomes unstable and
then cascades down the shoreward face of the wave. In plunging breakers, the crest of the wave curls
over the face of the wave and falls into the base, what surfers refer to as pipelines. In collapsing waves,
the crest remains stable and unbroken while the lower part of the shoreward face steepens and then
falls to produce a turbulent flow. Surging waves practically don’t break, as the front face of the wave
just advances towards the beach. The surf similiarity parameter, ξo (Eq. 1), is typically used to classify
the waves based on wave height Ho and period Lo (Demirbilek and Vincent, 2002). However, the slope
parameter So (Eqn 2) can also be used and has a 99.9% correlation to the surf similarity parameter. This
is the parameter that was used in this experiment as it is in a form that can be used for solitary waves by
substituting an approximation for Lo (Eqn 3) since solitary waves are infinite in wave length. (Grilli et al.
1997). The slope parameter was used because it is derived from the Boussinesq equation and therefore
considered to be a mathematically derived as opposed to experimentally. After calculating So, the
following guidelines were used in determining the breaker types of the waves in this experiment:
surging breaking= 0.3

Table 2: Bedform nomenclature and roughness coefficients
Bedform configurations
Name
Description
k
(cm)
w
(cm)
Roughness Ratio
(w/k)
BR1 Small bedform, closely spaced, on flat reef 3.8 30 7.89
BR2 Large bedform, closely spaced, on flat reef 7.6 30 3.95
BR3 Large bedform, widely spaced, on flat reef 7.6 68 8.95
BR4 Small bedform, widely spaced, on flat reef 3.8 68 17.89
BS1 Small bedform, closely spaced, on beach slope 3.8 30 7.89
BS2 Large bedform, closely spaced, on beach slope 7.6 30 3.95
BS3 Large bedform, widely spaced, on beach slope 7.6 68 8.95
BS4 Small bedform, widely spaced, on beach slope 3.8 68 17.89
BN No bedform, smooth concrete beach and reef 0 0 0
3.5 Video Capture
Videos were taken of the breaking and crashing of the waves at 30 fps. The breaking properties of wave
height at breaking (Hb), distance of breaking (db) and distance of crashing (dc) were manually
determined and recorded by using a 0.5m x 0.5m grid that was painted on the back of the tank wall as a
reference (Figure 6). The breaking point was characterized as the point where "the wave front has a
vertical tangent" and the crashing point as where the "touchdown of breaker jet on the free surface"
occurs (Smith 2002). A database was made of all the movies and breaking information, and this
contribution to the project as a whole is considered to be significant.
Figure 6: Wave breaking, bedform configuration, and grid used to measure wave parameters.
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4. Results
Since the wave breaking geometry was determined manually using a grid that was of a low resolution,
the measurements could only be made to within 0.25m, giving a maximum error of ±0.125m. Since the
scale of this experiment was on the order of tens of meters, the possible maximum error was not
considered significant. Because a normal digital camera was used, the video only captured the
movement at 30 fps. This could cause a small source of error since the wave breaking point could have
occurred between frames. If the breaking point was between two frames, the difference in the point of
breaking between the frames was no more than 0.125m, again making the error insignificant.
All relationships and graphics were made using Ho’ as the independent variable except for those
relationships being compared to the previous literature. Following the standard method to describe
hydraulic experiments, all variables were turned into ratios.
While the original intent was to use all of the trials in every different experimental setup, it was difficult
to determine the breaking point when the waves were very small (Ho’= 0.05 or 0.1). After calculating
the slope parameter So (Eqn 2), the reason for difficulty was found. Waves with Ho’ ≤0.15 were
considered surging instead of plunging (Table 1), indicating that these waves did not have a defined
breaking point. Consequently, surging waves were not considered in this study. Out of the eight
bedform configurations, three were left out of data analysis due to time constraints. Blank surface trials
were also omitted as they were run after this paper was written. While data from all water levels was
analyzed, only data from water level 20cm is shown in the majority of this report.
4.1 Roughness
The roughness altered the breaking behavior of the waves. The bedforms slowed the waves, causing
them to lose energy and consequently affecting the breaking parameters (Hb, hb, db, dc). The flat reef
bedforms had minimal affect on the breaking parameters however since they were placed beyond the
zone where the waves usually broke. The wave height at breaking (Hb) was significantly lower when the
bedforms were on the slope (Figure 7) and the waves also broke and crashed sooner than when the
roughness was on the reef flat (Figures 8 and 9). Of the different bedform configurations on the slope,
BS2 had the lowest roughness coefficient and therefore was considered the roughest (Table 2). As seen
in Figures 8 and 9, the waves that propagated over BS2 had the smallest breaking and crashing
distances, indicating that the energy had dissipated the most. The difference in roughness in BS1 and
BS3 was very similar, and therefore they behaved almost identically. Since the reef roughness didn’t
affect the breaking behavior significantly, BR3 and BR4 also behaved similarly. The blank trials would
have been a useful addition to this analysis as they would have given insight into exactly how the
bedforms affected the waves.
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Figure 7: The bedforms over the reef (BR3 and BR4) show higher wave breaking heights than the bedforms over the slope
(BS1, BS2 and BS3). The difference in breaking index becomes more obvious as waves become larger.
Figure 8: Roughness on the slope (BS1, BS2, BS3) consistently caused the waves to break sooner as seen by the lower values
of breaking distance (db). BS2 presented the roughest surface, and therefore had the lowest db values.
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Figure 9: Roughness on the slope (BS1, BS2, BS3) consistently caused the waves to crash sooner as seen by the lower values
of crashing distance (dc).
4.2 Reef Geometry
The bottom bathymetry of the wave flume was modeled after a reef and had a significant effect on the
experiment. The steep slope of 1:12 followed by a flat reef produced results that showed a higher
breaking index and lower breaking water depth compared to studies done on a mild slope with no reef
crest (Grilli et al. 1997).
A breaking index of Hb/hb=0.80 for solitary waves is commonly used (Smith, 2002), however it has been
found to be inaccurate for reef bathymetry. A more improved, yet still empirical, relationship was found
by Grilli (1997) as Hb/hb=0.841exp(6.421So). Using this formula, the values of Hb/hb for this experiment
should have ranged from 0.94 to 1.01. However this study shows a significantly higher breaking index
(Figure 10). The mean index was Hb/hb= 2.878 with a standard deviation of ±0.560. These results are
most likely due to the geometry of the reef with the steep slope followed by flat surface.
By comparing the data from this experiment to an empirically derived formula for the breaking water
depth for solitary plunging breakers hb/ho= 0.149/(So/Ho’)^0.523 (Grilli et al 1997) , the breaking depth
was found to be consistently lower (Figure 11). The steep slope and reef flat were the cause of this
behavior.
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Figure 10: The breaking index vs. So (Eqn. 2) showing higher Hb/hb values than the ones found by the empirical relationship
developed by Grilli et al , 1997
Figure 11: The breaking depth vs. So/Ho’ showing lower breaking depth values than Grilli et al , 1997, experiments showed
5. Final Thoughts
The roughness and reef crest bathymetry altered the breaking behavior of the waves.
Because the behavior of the waves changed over various bedform configurations, roughness was proven
to have an effect on wave breaking parameters. When the roughness was installed before the waves
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8. References
Grilli, S.T. Svendsen I.A. and Subramanya, R. [1997] “Breaking Criterion and Characteristics for Solitary
Waves on Slopes,” Journal of Waterway, Port, and Coastal Engineering 123(3), 102-112
Hsiao, S.-C. et al. [2008] “On the evolution and run-up of breaking solitary waves on a mild sloping
beach,” Coastal Engineering 55, 975-988
Demirbilek, Z. and Vincent, L. [2002]. Coastal Hydrodynamics. In: Demirbilek, Z., Coastal Engineering
Manual, Part 2 , Water Wave Mechanics Chapter II-1 , Engineer Manual 1110-2-1100, U.S. Army Corps of
Engineers, Washington, DC.
Smith, J. [2002]. Coastal Hydrodynamics. In: Demirbilek, Z., Coastal Engineering Manual, Part 2 , Surf
Zone Hydrodynamics Chapter II-4 , Engineer Manual 1110-2-1100, U.S. Army Corps of Engineers,
Washington, DC.
National Geographic News [2005], “Tsunamis: Facts about Killer Waves”.
http://news.nationalgeographic.com/news/2004/12/1228_041228_tsunami.html
Young, J. and Xiao, H. [2008]. “Enhanced Sediment Transport due to Wave-Soil Interactions,”
Proceedings of 2008 NSF Engineering Research and Innovation Conference, Knoxville, Tennessee
SOEST. www.soest.hawaii.edu, 2009
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