Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 9
Fig. 6. A sketch of triangular grid for modeling typhoon-induced storm tide
4.1.2 Current velocity
It is clearly seen from F igures 7 and 8 that the maximum tidal ranges occur at the Ganpu
station (T4). Thus, it is expected that the maximum tidal current may occur near this
region. The tidal currents were measured at four locations H1-H4 across the estuary near
Ganpu. These measurements are used to verify the numerical model. Figures 9 and 10 are
the comparison between simulated and measured depth-averaged velocity magnitude and
direction for the spring and neap tidal currents, respectively. It is seen that the flood tidal
velocity is clearly greater than the ebb flow velocity for both the spring and neap tides. The
maximum flood velocity occurs at H2 with the value of about 3.8 m/s, while the maximum
ebb flow velocity is about 3.1 m/s during the spring tide. During the neap tide, the maximum
velocities of both the flood and ebb are much less than those in the spring tide with the value
of 1.5 m/s for flood and 1.2 m/s for ebb observed at H2. The maximum relative error for
the ebb flow is about 17%, occurring at H2 during the spring tide. For the flood flow the
maximal relative error occurs at H3 and H4 for both the spring and neap tides with values
being about 20%. In general, the depth-averaged simulated velocity magnitude and current
direction agree well with the measurements, and the maximal error percentage in tidal current
is similar as that encountered in modeling the Mahakam Estuary (Mandang & Yanagi, 2008).
187
Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China
10 Will-be-set-by-IN-TECH
Fig. 7. Comparison of the computed and measured spring tidal elevations at stations T2-T6.
−:computed;◦:measured
188
Hydrodynamics – Natural Water Bodies
Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 11
Fig. 8. Comparison of the computed and measured neap tidal elevations at stations T2-T6. −:
computed;
◦:measured
189

at 18:00 of 29/08/1981 (Beijing Mean Time). In general, the predicted wind directions agree
fairly well with the available measurement. However, it can be seen that calculated wind
speeds at these two stations are obviously smaller than o bservations in the early stage of
cyclonic development and then slightly higher than observations in later development. The
averaged differences between calculated and observed wind s peeds are 2.6 m/s at Daji station
and 2.1 m/s at Tanxu station during Typhoon Agnes. This discrepancy in wind speed is due
to that the symmetrical cyclonic model applied does not reflect the asymmetrical shape of
near-shore typhoon.
4.2.2 Storm surge
Figure 15 displays the comparison of simulated and measured tidal elevations at Daji station
and Tanxu station, in which the starting times of x-coordinate are both at 18:00 on 29/08/1981
(Beijing Mean Time). It can be seen from Figure 15 that simulated tidal elevation of high
tide is slightly smaller than measurement, which can be directly related to the discrepancy of
calculated wind field (shown in Figures 13 and 14). A series of time-dependent surge setup,
the difference of tidal elevations in the storm surge m odeling and those in purely astronomical
tide simulation, are used to represent the impact of typhoon-generated storm. Figure 16
having a same starting time in x-coordinate displays simulated surge setup in Daji station
and Tanxu station. There is a similar trend in surge setup development at these two stations.
The surge setup steadily increases in the early stage (0-50 hour) of typhoon development, and
then it reaches a peak (about 1.0 m higher than astronomical tide) on 52nd hour (at 22:00
on 31/08/1981). The surge setup quickly decreases when the wind direction changes from
north-east to north-west after 54 hour. In general, the north-east wind pushing water into the
Hangzhou Bay significantly leads to higher tidal elevation, and the north-west wind dragging
water out of the Hangzhou Bay clearly results in lower tidal elevation. The results indicate
that the typhoon-induced external forcing, especially wind stress, has a significant impact on
the local hydrodynamics.
192
Hydrodynamics – Natural Water Bodies
Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 15
Fig. 11. Comparison of the computed and measured spring current velocities at different

geometrical shape and shallow depth and is mainly controlled by the M
2
harmonic
constituent. The presence of tropical typhoon makes the tidal hydrodynamics in the
Hangzhou Bay further complicated.
2. The tidal range increases significantly as it travels from the lower estuary towards the
middle estuary, mainly due to rapid narrowing of the estuary. The tidal range reaches the
maximum at Ganpu station (T4) and decreases as it continues traveling towards the upper
estuary.
3. The flood tidal velocity is clearly greater than the ebb flow velocity for both the spring and
neap tides. The maximum flood velocity occurs at H2 with the value of about 3.8 m/s,
while the maximum ebb flow velocity is about 3.1 m/s during the spring tide. During the
neap tide, the maximum velocities of both the flood and ebb are much less than those in
the spring tide with the value of 1.5 m/s for flood and 1.2 m/s for ebb observed at H2.
4. The vertical distributions of current velocity at stations H1 and H4 show that the current
magnitude obviously decreases with a deeper depth (from sea surface to 0.8D), while the
flow direction remains the same.
5. Tropical cyclone, in terms of wind stress and pressure gradient, has a significant impact on
its induced storm surge. In general, the north-east wind pushing water into the Hangzhou
Bay significantly leads to higher tidal elevation, and the north-west wind dragging water
out of the Hangzhou Bay clearly results in lower tidal elevation.
6. References
Cao, Y. & Zhu, J. “Numerical simulation of effects on storm-induced water level after
contraction in Qiantang estuary,” Journal of Hangzhou Institute of Applied Engineering,
vol. 12, pp. 24-29, 2000.
Chang, H. & Pon, Y. “E xtreme statistics for minimum central pressure and maximal wind
velocity of typhoons passing around Taiwan,” Ocean Engineering, vol. 1, pp. 55-70,
2001.
Chen, C., Liu, H. & B eardsley, R. “An unstructured, finite-volume, three-dimensional,
primitive equation ocean model: application to coastal ocean and estuaries,” Journal

205-247, 2001.
Wang, C. “Real-time modeling and rendering of tidal in Qiantang Estuary,” International
Journal of CAD/CAM, vol. 9, pp. 79-83, 2009.
Xie, Y., Huang, S., Wang, R. & Zhao, X. “Numerical simulation of effects of reclamation in
Qiantang Estuary on storm surge at Hangzhou Bay,” The Ocean Engineering,vol.
25(3), pp. 61-67, 2007.
198
Hydrodynamics – Natural Water Bodies
10
Experimental Investigation on Motions
of Immersing Tunnel Element under
Irregular Wave Actions
Zhijie Chen
1
, Yongxue Wang
2
, Weiguang Zuo
2
,
Binxin Zheng
1
and Zhi Zeng
1
, Jia He
1

1
Open Lab of Ocean & Coast Environmental Geology,
Third Institute of Oceanography, SOA
2


Hydrodynamics – Natural Water Bodies

200
method. The motion responses of the tunnel element and the tensions acting on the
controlling cables are tested.
The time series of the motion responses, i.e. sway, heave and roll of the tunnel element and
the cable tensions are presented. The results of frequency spectra of tunnel element motion
responses and cable tensions for irregular waves are given. The influences of the significant
wave height and the peak frequency period of waves on the motions of the tunnel element
and the cable tensions are analyzed. Finally, the relation between the tunnel element
motions and the cable tensions is discussed.
2. Physical model test
2.1 Experimental installation and method
The experiments are carried out in a wave flume which is 50m long, 3.0m wide and 1.0m
deep. The sketch of experimental setup is shown in Fig. 1. Assuming the movements of the
barges on the water surface are small and can be ignored, the immersion of the tunnel
element is directly done by the cables from the fixed trestle over the wave flume.
The immersed tunnel element considered in this study is 200cm long, 30cm wide and 20cm
high, which is a hollow cuboid sealed at its two ends. The tunnel model is made of acrylic
plate and concrete and the cables are modeled by springs and nylon strings that are made to
lose their elasticity. Fig. 1. Sketch of experimental setup
It is known that the immersion of the tunnel element in practical engineering is actually
done by the ballast water, namely negative buoyancy, inside the tunnel element. The weight
of the tunnel element model used in this experiment is measured as 1208.34N. When the
model is completely submerged in the water, the buoyancy force acting on it is 1176.0N. So
the negative buoyancy is equal to 32.34N, which is 2.75 percent of the buoyancy force of the

6
7
00.511.522.5
tension (kg)
extension (cm)
d=10cm
d=30cm
d=50cm

Fig. 2. Relations between the elastic force and the spring extension
The CCD (Charge Coupled Device) camera is utilized to record the motion displacements of
the tunnel element during its interaction with waves. Two lights with a certain distance are
installed at the front surface of the tunnel element, as shown in Fig. 3. When the tunnel
element moves under irregular wave actions, the positions of the two lights are recorded by
the CCD camera. Finally, the sway, heave and roll of the tunnel element are obtained from
the CCD recorded images by the image analysing program. Fig. 3. Photo view of the tunnel element at the wave flume. (a) wave is propagating over the
tunnel element; (b) the tunnel element and CCD
2.2 Simulation of wave spectra
In the experiment, Johnswap spectrum is chosen as the target spectrum to simulate the
physical spectrum, and two significant wave heights, H
s
=3.0cm and 4.0cm, and three peak
frequency periods of waves, T
p
=0.85s, 1.1s and 1.4s are considered. As examples, two groups
of wave conditions, i.e. H
s

0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0123
f
(Hz)
S (
f
)
target spectrum
physical spectrum

(a) H
s
=3.0cm, T
p
=1.4s (b) H
s
=4.0cm, T
p
=1.1s
Fig. 4. Measured and target spectrum
3. Experimental results and discussion


203
-4
-3
-2
-1
0
1
2
3
4
0 1020304050607080
t(s)
η (cm)
heave

-8
-6
-4
-2
0
2
4
6
8
10
0 1020304050607080
t(s)
θ (°)
roll


Hydrodynamics – Natural Water Bodies

204
0
2
4
6
8
10
12
14
16
18
20
00.511.52
spectral density (cm
2
·s)
fre
q
uenc
y

(
s
-1
)
sway


·s)
frequency (s
-1
)
roll

a. d=10cm 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
00.511.52
spectral density (cm
2
·s)
frequency (s
-1
)
sway

0

uenc
y

(
s
-1
)
roll

b. d=30cm
Experimental Investigation on Motions of
Immersing Tunnel Element under Irregular Wave Actions

205
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2
spectral density (cm
2
·s)
frequency (s
-1
)
sway

0.3
0.35
012
spectral density (degree
2
·s)
frequency (s
-1
)
roll

c. d=50cm
Fig. 6. Frequency spectra of the tunnel element motion responses for different immersing
depths (H
s
=4.0cm, T
p
=1.1s)
3.1.3 Influence of the significant wave height on the tunnel element motions
The results of the frequency spectra of the tunnel element motion responses for different
significant wave heights in the test conditions d=30cm and T
p
=1.1s are shown in Fig. 7. From the
figure, it is seen that the shapes of the frequency spectrum curves of the tunnel element motion
responses are very similar for different significant wave heights, while just the peak values are
different. Corresponding to the large significant wave height, the peak value is large, as well
large is the area under the motion response spectrum. Apparently, the motion responses of the
tunnel element are correspondingly large for the large significant wave height.

sway

s
=4.0cm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2
frequency(s
-1
)
spectral density(cm
2
·s)Hydrodynamics – Natural Water Bodies

206

roll
H
s
=3.0cm
H
s
=4.0cm

larger is the peak frequency period of waves, the larger are the motion responses of the
tunnel element. sway

T
p
=0.85s
T
p
= 1.1s
T
p
= 1.4s
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
00.511.52

spectral density(cm
2
·s )

Experimental Investigation on Motions of
Immersing Tunnel Element under Irregular Wave Actions

207
roll
T
p
=0.85s
T
p
= 1.1s
T
p
= 1.4s
0
5
10
15
20
25
30
35
40
45
00.511.52
frequency(s

tensions of the cables C11 and C12 at the onshore side are very similar, as well similar are
those of the cables C21 and C22 at the offshore side. It shows that under the normal incident
irregular wave actions the tunnel element does only two-dimensional motions. This can also
be observed in the experiment from the movement of the tunnel element.
3.2.2 Cable tensions for the different immersing depth of the tunnel element
Fig. 10 shows the results of the frequency spectra of the cable tensions in the wave conditions
H
s
=4.0cm and T
p
=1.1s for different immersing depths of the tunnel element. From the peak
values of the frequency spectra curves and the areas under the frequency spectra, it is seen that
the tensions acting on the cables are comparatively large in the case of comparatively small
immersing depth, as is corresponding to the motion responses of the tunnel element.
Furthermore, the peak values and the areas of the frequency spectra of the cable tensions at the
offshore side are all larger than those of the cable tensions at the onshore side for different
immersing depths. It indicates that the total force of the cables at the offshore side is larger

Hydrodynamics – Natural Water Bodies

208
than that of the cables at the onshore side. It is also shown that in the figure there are at least
two peaks in the curves of the frequency spectra of the cable tensions, which are respectively
corresponding to the wave-frequency motions and low-frequency motions of the tunnel
element. When the tunnel element is at the position of a relatively small immersing depth, the
frequency spectra of the cable tensions have other small peaks besides the two peaks at the
wave frequency and the low frequency. It illustrates that the case of the forces generating in
the cables is more complicated for the comparatively strong motion responses of the tunnel
element under the wave actions when the immersing depth is relatively small.


2.5
3
3.5
0 20 40 60 80 100 120 140 160 18
0
t(s)
F(kg)
C21

Experimental Investigation on Motions of
Immersing Tunnel Element under Irregular Wave Actions

209
0
0.5
1
1.5
2
2.5
3
3.5
0 20 40 60 80 100 120 140 160 180
t(s)
F(kg)
C22

Fig. 9. Time series of tensions acting on the cables (d=30cm, H
s
=4.0cm, T
p

2.5
3
3.5
00.511.522.533.5
spectral density (kg
2
·s)
frequency (s
-1
)
offshore side

a. d=10cm

0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
00.511.522.533.5
spectral density (kg
2
·s)
fre

b. d=30cm

Hydrodynamics – Natural Water Bodies

210
0
0.005
0.01
0.015
0.02
0.025
0.03
00.511.522.533.5
spectral density (kg
2
·s)
frequency (s
-1
)
onshore side

0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04

s
=4.0cm is larger
than that for H
s
=3.0cm. Therefore, the larger is the significant wave height, the larger are the
cable tensions accordingly. This is corresponding to the case that the motion responses of
the tunnel element are larger for the larger significant wave height. When the significant
wave height increases, the wave effects on the tunnel element increase. Accordingly, the
forces acting on the cables also become larger.
onshore side
H
s
=3.0cm
H
s
=4.0cm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2


Fig. 11. Frequency spectra of the cable tensions for different significant wave heights
(d=30cm, T
p
=1.1s)
Experimental Investigation on Motions of
Immersing Tunnel Element under Irregular Wave Actions

211
3.2.4 Influence of the peak frequency period on the cable tensions
The results of the frequency spectra of the cable tensions for different peak frequency
periods of waves in the test conditions d=30cm and H
s
=3.0cm are shown in Fig. 12. It is
seen that the cable tensions are largely influenced by the peak frequency period. The peak
values of the frequency spectra of the cable tensions increase rapidly as the peak
frequency period increases. Corresponding to the case of the motion responses of the
tunnel element for different peak frequency periods, the larger is the peak frequency
period, the larger are also the cable tensions. For different peak frequency periods, the
frequency spectra of the cable tensions all have a peak at the corresponding frequency.
Besides, from the figure, it can be observed that the peaks of the frequency spectra at the
lower frequency are obvious when the peak frequency period T
p
=1.4s. This reflects that
the low-frequency motions of the tunnel element become large with the increase of the
peak frequency period of waves.
onshore side

T
p
= 1.1s
T
p
= 1.4s
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.5 1 1.5 2
frequency(s
-1
)
spectral density(kg
2
·s )
Fig. 12. Frequency spectra of the cable tensions for different peak frequency periods of
waves (d=30cm, H
s
=3.0cm)