International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Measurement of Infragravity Edge Waves on the East Coast of

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


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The instantaneous surface elevation of the edge wave


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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


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Formation Of Cusps By Edge Waves


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For most harbors, the harbor entrance is facing the open sea


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Examples:harbor entrance is facing the open sea


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Examples:harbor entrance is facing the open sea


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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.


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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


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Series of offshore detached breakwaters constructed outside the harbor, resulting in delaying the resonance inside for more than one hour


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侷限波與滲漏波


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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


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The locations of three stations N

(north), S (south) and M

(main) near the entrance of Hua-

Lien Harbor


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The traditional approach to edge wave measurement requires some

twenty instruments


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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


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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


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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

��


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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.


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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



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•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


gh


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Stations N and M are close to

the harbor entrance where a progressive wave could be reflected by the breakwaters and

form standing waves


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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.


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Typhoons in 2005 are too close to Hua-Lien and hence the direction of the

typhoon waves cannot be determined


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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


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Typhoon Kaemi (23-26 July, 2006) affected the Hua-Lien coast from five

o’clock of July 23rd.


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The time series of pressure, eastward and northward flow measured at station S


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The IMF's of the pressure time series recorded at 6 AM of July 23rd


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•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


gh


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The spectrum inside the harbor during Typhoon Tim (July, 1994), is concentrated in two period ranges:

70-120 sec and 120-190 sec.


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05:00, 23 July


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• 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.


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06:00, 23 July


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• 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.


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19:00, 24 July


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19:30, 24 July


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• 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.


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05:00, 25 July


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12:00, 25 July


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09:00, 25 July


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• 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


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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.


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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.


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Thank you for your attention歡迎提問

Documents

International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Measurement of Infragravity Edge Waves on the East Coast of