extreme wave runup

Laboratory Investigation of Wave Runup on a
Prototype Scale Sand Barrier
C.E.
1
Blenkinsopp ,
A.
2
Matias ,
D.
3
Howe ,
B.
4
Castelle ,
V.
4
Marieu
1Department
of Architecture and Civil Engineering, University of Bath; 2CIMA - Universidade do Algarve; 3Water Research
Laboratory, School of Civil and Environmental Engineering, University of New South Wales; 4Université Bordeaux 1, CNRS
EXTREME WAVE RUNUP
SWASH PROFILES
BORE COLLAPSE MODEL (cont)
Wave runup R describes the elevation of the interface
between land and water and is measured vertically
relative to the still water line (Figure 1).
Accurate predictions of wave runup are vital because
extreme runup during storm conditions can:
• present a danger to coastal infrastructure;
• lead to dune overtopping and erosion;
• overwash barrier beaches, and;
• lead to significant morphological change.
Runup can be divided into a quasi-steady wave setup
component <h> and time-varying swash component S.
Extreme wave runup was defined as R2% which
corresponds to the elevation exceeded by 2% of waves
during a test.
Measured data was compared against 11 commonly
used parameterisations derived from laboratory and
field data.
It was found that the laboratory-derived equations
Hedges and Mase (2004) (r2 = 0.923; RMSE = 0.094
m) performed best, though the empirical coefficients
were adjusted for the current data:
𝑅2% = 0.39 + 0.795ξ𝑜 𝐻𝑜
(1)
where:
Ho = deepwater wave height
ξ𝑜 = deepwater Irribarren number
The LiDAR enables high-resolution measurements of
the swash free-surface to be obtained at 35Hz (Figure
4). The LiDAR results were compared with point
measurements from ultrasonic altimeters and pressure
sensors with good agreement.
If this velocity is used to drive a ballistic swash model
based on the special solution of the Non-Linear
Shallow Water Equations developed by Shen & Meyer
(1963), the maximum swash excursion from the point
of bore collapse is:
𝐻
(2)
1
𝐿𝑜 2
and:
Lo = deepwater wavelength
b = beachface gradient
Figure 1. Definition of wave runup
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0.8
A
𝑆𝑠 =
B
Depth (m)
0.7
0.5
0.3
C
0.2
86
88
90
92
Cross shore distance (m)
94
Figure 4. Contour plots of time-varying depth for
three irregular swash events of varying magnitude.
Analysis of swash profiles for multiple swash events
during regular and irregular waves found that when
normalised by depth, length and duration, swash
profiles demonstrate clear self-similarity (Figure 5).
1.0
WAVE RUNDOWN
While R2% is commonly reported in the literature,
much less information is available regarding the
rundown limit.
The rundown limit Rd2% - here defined as the elevation,
relative to SWL below which only 2% of measured
swash minima transgress - indicates the lower limit of
swash processes.
-0.5
Figure 2. The instruments measured the time-varying
water surface in the swash zone, creating high
resolution swash depth profiles through time. LiDAR
uses light to detect the water surface and the sand,
while the acoustic altimeters use sound.
RESEARCH POSTER PRESENTATION DESIGN © 2012
www.PosterPresentations.com
0.5
t* = 0.50
0.5
0.0
1.0
t* = 0.75
0.5
0.0
1.0
t* = 1.00
0.5
0.0
0.0
0.2
0.4
0.6
0.8
Dimensionless cross shore distance, x*
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
Bore Collapse Height, Hbore (m)
0.6
0.7
Figure 6. Vertical runup excursion as a function of
bore height at collapse, Hbore.
1.0
References
Baldock, T.E., Holmes, P., 1999. Simulation and prediction of swash
oscillations on a steep beach. Coast. Eng. 36(3), 219-242.
Hedges, T.S., Mase, H., 2004. Modified Hunt's equation incorporating
wave setup. J. Waterw. Port. C-ASCE. 130, 109-113.
Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach Part 3. Runup. J. Fluid Mech. 16, 113–125.
Acknowledgements
-1
-1.5
0.5
t* = 0.25
0.0
1.0
1.5
• Extreme runup is a simple function of Irribarren
number and offshore wave height.
• Rundown limit correlates well with Irribarren
number and is typically below SWL.
• Initial runup velocity and hence swash excursion
can be predicted by assuming a conversion of
potential to kinetic energy at bore collapse.
• Swash surface profiles for regular and irregular
waves are self-similar.
Figure 5. Dimensionless profiles for the swashes in
Figure 4. Blue, green and red lines correspond to
panels A, B, and C, respectively. Profiles for seven
additional swashes are also shown (thin grey lines).
0
Rd2% (m)
Experiments were undertaken at the Delta Flume,
Netherlands (dimensions = 240m x 5m x 7m).
Instrumentation for runup measurement was installed
above a prototype-scale sand-barrier (Figure 2):
• 45 ultrasonic altimeters
• 2 scanning LiDAR
• 3 camera systems
In addition numerous other instruments were installed
including acoustic doppler velocimeters,
electromagnetic current meters, ripple profilers,
sediment profilers, pressure sensors etc, etc etc!
85 experimental runs were completed with Hs in the
range 0.6 to 1.2 m and Tp between 8 and 12 seconds.
Dimensionless depth, d*
0.5
EXPERIMENTAL SETUP
(5)
CONCLUSIONS
t* = 0.00
0.0
1.0
𝐶 2 𝐻𝑏𝑜𝑟𝑒
2
Figure 6 shows strong correlation between Ss and Hbore
where C is in the range 1.95 to 2.25.
Vertical Runup Excursion, Ss (m)
𝜉𝑜 =
𝛽
Time (mm:ss)
INTRODUCTION
BORE COLLAPSE MODEL
1
1.5

2
2.5
3
Figure 3. Rd2% as a function of Irribarren no.
Figure 3 demonstrates a strong correlation between the
measured rundown limit and the deepwater Irribarren
number and the equation of the linear regression is:
𝑅𝑑2%
𝐻𝑜
= 0.476ξ𝑜 − 0.30
(3)
The high resolution measurements of free-surface
profile enable the bore height at the moment of
collapse on the beach Hbore to be estimated for every
incident wave.
If it is assumed that there is a conversion of potential
to kinetic energy, the initial swash velocity can be
estimated according to Baldock & Holmes (1999) as:
𝑢𝑜 = 𝐶 𝑔𝐻𝑏𝑜𝑟𝑒
where for a perfect conversion C = 2.0.
(4)
This work was supported by the European Community's 7th Framework
Programme through a HYDRALAB IV grant, contract no. 261520.
Additional support was provided by an Australian Research Council
Discovery Grant (DP110101176).