Individual Wave Analysis

1
PRESSURE GRADIENTS OVER A BARRED BEACH
Sungwon Shin (shinsu_at_engr.orst.edu), Takayuki
Suzuki, William Boylston, and Daniel T. Cox O.H.
Hinsdale Wave Research Laboratory, College of
Engineering, Oregon State University
http//wave.oregonstate.edu
Exceedance Probability Madsen (1974) proposed
that large horizontal pressure gradients can
cause a momentary failure or instability of bed
material. The paper suggested a critical value of
the pressure gradient for this failure of 0.5,
based on common assumptions for fully saturated
sands.
Skewness and Asymmetry of Pressure Gradients and
Accelerations

• Motivation/Objectives
• Sandbars play an important role in beach
  morphology and wave climate. It has been proposed
  that onshore sandbar migration is affected by
  wave-induced acceleration and offshore migration
  occurs when undertow is dominant (Elgar et al,
  2001). However, onshore sandbar migration is not
  well-understood. Recent model studies (Rakha et
  al., 1997 Drake and Calantoni, 2001 Karambas
  and Koutitas, 2002 Long and Kirby, 2003) include
  acceleration skewness for either the entire time
  series or on a wave-by-wave basis to simulate
  sediment transport. In the present study,
  cross-shore pressure gradients were observed in a
  large-scale wave flume over a barred beach and
  compared with the local wave induced fluid
  acceleration to get a better understanding of
  these processes.
• The objectives of this study are
• To obtain a synoptic data set of the free surface
  elevation, pressure gradients, and fluid
  velocities on a barred beach for a random wave
  case.
• To compare the pressure gradient skewness with
  the acceleration skewness at each cross-shore
  location for the entire time series and on a
  wave-by-wave basis to test sediment transport
  model assumptions.
• To investigate the probability of the pressure
  gradient exceeding a critical value for
  momentary failure of the sea bed.
• Experimental Setup
• The experiment was carried out in the Large Wave
  Flume of O. H. Hinsdale Wave Research Laboratory
  at Oregon State University (Figure 1). The flume
  is 104 m long, 3.7 m wide, and 4.3 m deep and can
  generate a maximum wave height of 1.6 m. The
  bathymetry approximated the bar geometry observed
  on Oct 11, 1994, of the Duck94 field experiments
  at 13 scale.

Since the local fluid acceleration outside the
bottom boundary layer is related to the pressure
gradient, many modelers have used fluid
acceleration to predict sediment transport. In
the present study, the dimensionless pressure
gradient is defined as
(a)
(a)
(b)
L 1
L 5
L 8
L5
L8
L1
The exceedance probability (PE) can be used to
investigate the occurrence probability of
momentary failure based on this critical value
(Cox et al, 1991). It can be modeled by a
Rayleigh distribution
(c)
and is compared to the local acceleration
measured at the same elevation. Skewness and
asymmetry statistics are computed in Figure 3.
(b)
(c)
(d)
(d)
(e)
Figure 3 Cross shore variation of skewness and
asymmetry of free surface, pressure, horizontal
velocity, ?P, and acceleration (du/dt) for
entire time series for L 1 L 9. Arrows refer to
details of Figure 4 5. Figure 3 (a) and (b)
shows that skewness and asymmetry of water
surface elevation, pressure, and near bottom
horizontal velocities have good correlation.
Also, horizontal velocity asymmetry, acceleration
and pressure gradient skewness using entire time
series were well correlated in most regions
(Figure 3 (c) and (d)).
(e)
(f)
L 5
Figure 6 PE of pressure gradients in both onshore
(blue) and offshore (red) direction (b d) and
contour plot of PE for L1 L9 (e) based on
unfiltered data . PE for Rayleigh distribution (b
d) is plotted vs ?P. Figure 6 (b) (d) show
that extreme values (?Pgt0.5) are greater in
offshore direction than onshore direction at L 5
but typical values (?Plt0.5) are smaller in
offshore direction than onshore direction.
Contour plot in Figure 6 (e) shows that, in most
cross-shore location except near the bar
location, pressure gradients in onshore direction
are larger than those in offshore direction.
Individual Wave Analysis How well do these
quantities compare on a wave-by-wave basis? Joint
distribution is used to examine hydrodynamic
quantities for the 354 individual waves (Figure 4
and 5). To consider larger waves which may
dominate the total and net sediment transport,
the analysis was repeated using only the 1/3
highest waves.
Four pressure transducers were mounted in a thin
plate oriented lengthwise along the center of the
tank, 1 cm from the bottom. Two Sontek ADVs were
collocated in the cross-shore direction and
measured the velocity at 1 cm and 5 cm from the
bottom.
Figure 4 Joint distribution of horizontal
velocity skewness vs. acceleration skewness (left
and center panels). Filled circles are the 1/3
highest waves and red open circles are smaller
waves than the 1/3 highest waves. Dashed lines
are the best fit using all waves (left panels)
and the 1/3 highest waves (center panels) Cross
shore variation of r2 value and slope of best fit
lines. Open circles are using all waves. Filled
circles are the 1/3 highest waves. (right
panels) Elgar, et al (2001) suggested that
acceleration skewness and velocity asymmetry are
related to onshore sediment movement. Figure 3
shows that these values are well correlated
except at L 8. However, the joint distribution
for individual wave in Figure 4 shows that
correlation between the two quantities are low in
both cases (all waves and 1/3 highest waves) near
the bar and L8. Cross-shore variation of r2
values, in spite of using 1/3 highest waves,
still do not improve.
L 1
L 1
Figure 7 Time series of unfiltered extreme case
indicated in Figure 6 at L 5.
This kind of event occurred under broken waves.
Magnified figure (left) of extreme event shows
that the signal is not noise and several data
points were involved in the event. The occurrence
of extreme events corresponds with large
horizontal velocity signal measured by ADV. This
result shows that extreme event of momentary
failure can be affected by intermittent
turbulence.
L 5
L 5

• Conclusions
• Large-scale, synoptic data of the pressure
  gradient on a barred beach for random waves were
  acquired.
• The skewness of the local fluid acceleration has
  a high correlation with that of the pressure
  gradient, when averaged over many waves.
• The correlation of the local fluid acceleration
  skewness with pressure gradient skewness is low
  when considered on a wave-by-wave basis, even for
  the 1/3 highest waves.
• Exceedance probability of ?P shows that extreme
  events occur over the bar and correspond to large
  velocities due to intermittent wave breaking.
• Acknowledgements
• This work was partially funded by the National
  Science Foundation under grants
• No. CMS-0086571, EEC-0244205 and OCE-0351741. The
  success of this project
• was due to the contributions of many, especially
  Terry Dibble and Chris Scott.
• References
• Cox. D. T., Kobayashi, N., and Mase, H. (1991).
  Effects of fluid accelerations on sediment
  transport in surf zones. Coastal Sediments 91,
  447-461.
• Drake, T. G., and Calantoni, J. (2001). Discrete
  particle model for sheet flow sediment transport
  in the nearshore. JGR-Oceans, 106 (C9),
  19,859-19,868.
• Elgar, S., Gallagher, E. L., and Guza, R. T.
  (2001). Nearshore sandbar migration.
  JGR-Oceans, 106 (C9), 11,623-111,627.
• Goring, D.G., and Nikora, V.I. (2002). Despiking
  Acoustic Doppler Velocimeter Data. J. Hydr.
  Engrg., 128(1), 117-126.
• Hoefel, F., and Elgar, S. (2003). Wave-induced
  sediment transport and sandbar migration.
  Science, 299, 1,885-1,887.
• Karambas, T. V., and Koutitas, C. (2002). Surf
  and swash zone morphology evolution induced by
  nonlinear waves. JWPCOE., 128 (3), ASCE,
  102-113.

L 8
L 8
Figure 5 Joint distribution of horizontal
pressure gradients skewness vs. acceleration
skewness (left and center panels). Filled circles
are the 1/3 highest waves and red open circles
are smaller waves than the 1/3 highest waves.
Dashed lines are the best fit using all waves
(left panels) and the 1/3 highest waves (center
panels) Cross shore variation of r2 value and
slope of best fit lines. Open circles are using
all waves. Filled circles are the 1/3 highest
waves. (right panels) Figure 5 shows that
horizontal pressure gradients have almost no
correlation with acceleration skewness for
individual wave. Therefore, the assumption that
pressure gradients are related to the local fluid
acceleration is questioned. A time dependent
phase resolving model which relies on the local
fluid acceleration skewness or asymmetry on a
wave-by wave basis may not accurately reflect the
basic physics.
L 1
L 1
L 5
L 5
Figure 1. Experimental setup and instrumentation
at the O. H. Hinsdale Wave Research Laboratory at
Oregon State University
Data Reduction The data were band passed filtered
to remove frequencies higher than 4 times the
spectral peak period. The velocity data were
despiked using the method of Goring and Nikora
(2002) and the pressure gradients were computed
using the 4 sensors by
L 8
L 8
L 5
u (cm/s)
Figure 5 shows that pressure gradient skewness is
not uniquely determined by the local fluid
acceleration. Therefore, sediment transport
models driven by the local fluid acceleration
skewness on a wave-by-wave basis may not
correctly represent the physical processes.
du/dt (cm/s2)
Figure 2. Example time series at L5 over the bar