Port and Harbor Engineering

Radianta TriatmadjaLecture note 4

WAVE and WAVE CLIMATES

Wind waves are generated by wind.Wind stress on water surface, transfers the

wind energy to the water and create waves

The waves energy and so the wave height depends on the wind energy transferred which is a function of :

Wind speed, wind duration and fetch

Coordinate system used in wave dynamic

X

Z

Z=0

0,0

peak

Mean sea level

78,-6.3

45, -h

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

Lk 2

Height =H

Linear Wave(Airy wave)

H kx t2cos( )

)cos(sinh

)(cosh2

tkxkhzhkH

xu

wz

H k h zkh

kx t

2

sinh ( )sinh

sin( )

)sin(sinh

)(cosh2

2

tkxkhzhkH

tu

Particle horizontal velocity

Particle vertical velocity

Particle horizontal acceleration

Water fluctuation

Particle trajectory

(x,z)

H k h z

khkx t

21

1cosh ( )sinh

sin( )

H k h z

khkx t

21

1sinh ( )sinh

cos( )

Particle trajectory

• What can be concluded from the fact that the particle is moving in circle ?

•

Pressure under waves

)cos(cosh

)(cosh2

tkxkhzhkHggzp

Dispersion Equation

2 gk khtanh

L gT hL

2

22

tanh

LhgTC

2tanh

2Wave celerity

Wave Length

Wave Energy

E gH Lt 2

8

Wind Waves

Fetch

Wind Speed

Wind duration (hrs)

H in meter

Wind Waves

Fetch

Wind Speed

Wind duration (hrs)

H in meter

Wave height

T in seconds

Wind Waves

Fetch

Wind Speed

Wind duration (hrs)

Fully developed sea

Wave height and duration

Adjusted Wind Speed

R

23.171.0 WA UU

7/1

1010

z

UU zAdjustment due to measurement above or below 10 meter

Adjustment if measurement is conducted inland

Adjustment to accommodate temperature difference

Wind Stress factor or adjusted wind speed

Wind Waves

Fetch

Wind Speed

Wind duration (hrs)

H in meter, is significant Wave Height

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.

2.682.031.601.421.00

1.681.281.000.890.63

1103350100

H33/HrmsHn/H100Hn/H33n %

Hmax = 0.707 H33 =

2

Energy Flux

F ECn

Wave Transformation

• Wave refraction (water depth variation)• Wave Shoaling (shallow water)• Wave defraction (obstruction)

Front Velocity

Lg

CkhkhCg

121

22sinh