international symposium on sediment transport and sedimentation on asian continental margins...
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International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Measurement of Infragravity Edge Waves on the East Coast of Taiwan using a
Single Instrument
Guan-Yu Chen, Hsiao-Ching Chien
Institute of Applied Marine Physics and Undersea Technology, National Sun Yat-Sen University
Hsiang-Mao Tseng
Institute of Harbor and Marine Technology
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The instantaneous surface elevation of the edge wave
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The importance of edge wave is first proposedwhen Crescentic Sandbar were noticed
邊緣波與沙嘴 /新月型沙洲的形成有關
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Formation Of Cusps By Edge Waves
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
For most harbors, the harbor entrance is facing the open sea
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Examples:harbor entrance is facing the open sea
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Examples:harbor entrance is facing the open sea
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Instead of facing the sea,the
Hua-Lien harbor is along the
long straight east coast of Taiwan
This specific layout of Hua-Lien harbor makes the
basin vulnerable to the influence of edge waves.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
When a typhoon moved northward from the southeast, the wave condition inside the Hua-Lien Harbor can be very dangerous Even when the center is far away
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Series of offshore detached breakwaters constructed outside the harbor, resulting in delaying the resonance inside for more than one hour
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
侷限波與滲漏波
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Bad News
Infragravity edge wave has never been observed in the east coast of Taiwan.
identifying the existence of edge waves is very helpful in designing countermeasures
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The locations of three stations N
(north), S (south) and M
(main) near the entrance of Hua-
Lien Harbor
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The traditional approach to edge wave measurement requires some
twenty instruments
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Scale Analysis
21( ) 2u u u p u u
t
��������������
Infragravity velocity component is of order 0.2m/s or smaller
Advection term can be neglected
The Earth rotates at about 10^-4/sec
Coriolis effect can be neglected
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Scale Analysis (2)
21( ) 2u u u p u u
t
��������������
Kinematic viscosity for water is less than 1 m^2/s
Time scale for Infragravity motion is 20-500 sec
The Earth rotates at about 10^-4/sec
Length scale for Infragravity edge wave is
which is of order 1000m. Viscosity can be neglected.
2
2
2 2(2 1) (2 1)
2
TL g n g n
k
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Scale Analysis (3)• For water depth around 20 m the friction in the
vertical direction is also negligible for infragravity waves
(1)
1v p
t y
(2)
海洋波動研究室
21( ) 2u u u p u u
t
��������������
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
If waves are generated far away along the coast, their direction is easy to determine
Although reflection of the shoreline is possible, these waves are basically progressive.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
If waves are generated far away along the coast, these waves are basically
progressive. • Specific Fourier components of dynamic
pressure and y-velocity are both proportional to exp(iky-it).The p-v relation is derived as
P V cVk
(3)
ω=2πT
k=2πL
海洋波動研究室
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
•1. For an infragravity leaky wave, the phase velocity is exactly the shallow water celerity
•2. For an edge wave
• where s is the constant bottom slope, T is the wave period and the integer n is the mode number
P gh V
(2 1)2
P gTn s
V
海洋波動研究室
gh
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Stations N and M are close to
the harbor entrance where a progressive wave could be reflected by the breakwaters and
form standing waves
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
If waves are generated far away along the coast, their direction is easy to determine
Although reflection of the shoreline is possible, these waves are basically progressive.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Typhoons in 2005 are too close to Hua-Lien and hence the direction of the
typhoon waves cannot be determined
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Track of Typhoon Kaemi is in the south of Hua-Lien; the edge wave feature is
significant even when the typhoon is 500 km away from Hua-Lien
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Typhoon Kaemi (23-26 July, 2006) affected the Hua-Lien coast from five
o’clock of July 23rd.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The time series of pressure, eastward and northward flow measured at station S
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The IMF's of the pressure time series recorded at 6 AM of July 23rd
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
•1. For an infragravity leaky wave, the phase velocity is exactly the shallow water celerity
•2. For an edge wave
• where s is the constant bottom slope, T is the wave period and the integer n is the mode number
P gh V
(2 1)2
P gTn s
V
海洋波動研究室
gh
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
The spectrum inside the harbor during Typhoon Tim (July, 1994), is concentrated in two period ranges:
70-120 sec and 120-190 sec.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
05:00, 23 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
• The observed pressure is proportional to the longshore velocity. The proportionality ratio is close to the theoretical relation with n=0 which corresponds to Stokes edge waves.
• The theoretical lines for the first three edge wave modes are drawn together to show the existence of a Stokes edge wave.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
06:00, 23 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
• To exclude the possibility of mistakenly interpreting a leaky wave as an edge wave, the maximum flow, instead of the longshore component of the infragravity wave, is used, with the shallow water celerity being used in computing the theoretical slope
• When the wave started to affect the Hua-Lien coast, the edge wave features are significant.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
19:00, 24 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
19:30, 24 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
• When the typhoon is close to the land, the p-u relation becomes much more complicated.
• Some cases show leaky wave features
• The wave energy is distributed in several modes.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
05:00, 25 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
12:00, 25 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
09:00, 25 July
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
• in the late stages of Typhoon Kaemi on 25 July show clear Stokes edge wave features again
• Lower mode edge waves propagate slower than plane leaky waves and are highly dispersive
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Summary
• The present p-v approach requires only a single instrument and hence is a much easier and cheaper method for measuring edge waves.
• By contrast, the traditional frequency- wavenumber approach needs 20 instruments.
International Symposium on Sediment Transport and Sedimentation on Asian
Continental Margins
Discussion
• The present approach implicitly assumes that at each frequency range the edge wave energy is concentrated in just one mode.
• For some engineering problems such as beach erosion and tsunami incidents, identifying the existence of edge waves is very helpful in designing countermeasures.