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Port and Harbor Engineering

Radianta Triatmadja

Lecture note 4

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WAVE and WAVE CLIMATES

Wind waves are generated by wind.

Wind stress on water surface, transfers thewind energy to the water and create

waves

The waves energy and so the wave heightdepends on the wind energy transferred

which is a function of :Wind speed, wind duration and fetch

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Coordinate system used in wave

dynamic

X

Z

Z=0

0,0

peak

Mean sea level

78,-6.3

45, -h

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Notations

T 2

Amplitude = a,

or H/2

Wave length (L)

Fluctuation =

Wave Period = T, Time required for the

wave to travel one wave length

L

k2

Height =H

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Linear Wave

(Airy wave)

H

kx t2

cos( )

)cos(sinh

)(cosh

2 tkxkh

zhkH

xu

w

z

H k h z

kh

kx t

2

sinh ( )

sinh

sin( )

)sin(sinh

)(cosh

2

2

tkxkh

zhkH

t

u

Particle

horizontalvelocity

Particle

vertical

velocity

Particle

horizontal

acceleration

Water

fluctuation

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Particle trajectory

(x,z)

H k h z

kh kx t2

11

cosh ( )

sinh sin( )

H k h z

khkx t

2

11

sinh ( )

sinhcos( )

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Particle trajectory

What can be concluded from the fact that

the particle is moving in circle ?

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Pressure under waves

)cos(cosh

)(cosh2

tkxkh

zhkHggzp

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Dispersion Equation

2 gk khtanh

LgT h

L

2

2

2

tanh

L

hgTC

2tanh2

Wave celerity

Wave Length

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Wave Energy

E gH Lt 2

8

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Wind Waves

Fetch

Wind

Speed

Wind duration

(hrs)

H in meter

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Wind Waves

Fetch

Wind

Speed

Wind duration

(hrs)

H in meter

Wave height

T in seconds

Wi d d ti

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Wind Waves

Fetch

Wind

Speed

Wind duration

(hrs)

Fully

developed

sea

Wave height and

duration

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Adjusted Wind Speed

R

23.1

71.0 WA UU

7/1

1010

zUU z

Adjustment due to measurement

above or below 10 meter

Adjustment if measurement

is conducted inland

Adjustment toaccommodate

temperature difference

Wind Stress factor

or adjusted windspeed

Wi d d ti

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Wind Waves

Fetch

Wind

Speed

Wind duration

(hrs)

H in meter, is significant Wave

Height

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Wave Height Statistic

Hs = H significant , the average of 33% highest

waves in the record

H10 = the average of 10% highest waves in the

record

Nln

Ratio between wave heights and H33 dan H100.

2.682.03

1.60

1.42

1.00

1.68

1.28

1.00

0.89

0.63

1

10

33

50

100

H33/HrmsHn/H100Hn/H33

n %

Hmax = 0.707 H33

=

2

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Energy Flux

F ECn

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Wave Transformation

Wave refraction (water depth variation)

Wave Shoaling (shallow water)

Wave defraction (obstruction)

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Front Velocity

Lg

Ckh

khCg

1

21

2

2sinh