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Port and Harbor Engineering Radianta Triatmadja Lecture note 4
WAVE and WAVE CLIMATES Wind waves are generated by wind. Wind stress on water surface, transfers the wind energy energy to the water and create waves The wav waves es energy and so the wav wave e height depends on the wind energy transferred which is a function of : W ind speed, wind wind duration and fetch
Coordinate system used in wave dynamic Z
peak Z=0 Mean sea level 0,0 78,-6.3
45, -h
X
Notations Height =H Amplitude = a, or H/2
Fluctuation =
Wave length (L) Wave Period = T, Time required for the wave to travel one wave length
k
2
T
2
L
Linear Wave (Airy wave) Water fluctuation Particle horizontal velocity Particle vertical velocity
Particle horizontal acceleration
H u x 2 w z
u H 2 2 t
H
cos( kx t )
2 cosh k ( h z ) sinh kh H 2
cos( kx t )
sinh k ( h z) sin( kx t ) sinh kh
cosh k (h z ) sinh kh
sin( kx t )
Particle trajectory (x,z)
H cosh k( h z1 ) 2
sinh kh
H sinh k( h z1 ) 2
sinh kh
sin( kx1
t )
cos( kx1 t )
Particle trajectory • What can be concluded from the fact that the particle is moving in circle ? •
Pressure under waves
H cosh k ( h z ) p gz g cos( kx t ) 2 cosh kh
Dispersion Equation
gk tanh kh 2
Wave Length
Wave celerity
L
2 h gT tanh 2 L
C
2
gT 2
tanh
2h L
W ave Energy Energy
gH
2
E t
8
L
Wind duratio d uration n (hrs) H in meter
W ind ind Waves
Wind Speed
Fetch
T in seconds H in meter
Wind Speed
Wind duratio d uration n (hrs)
W ind ind Waves
Wave height
Fetch
Wind duratio d uration n (hrs)
W ind ind Waves Wind Speed
Wave height and duration
Fully developed sea
Fetch
Adjusted Adjusted Wind W ind Speed 1/7
Adjustment due to measurement above or below 10 meter
10 U 1 0 U z z R
Adjustment if measurement is conducted inland
Adjustment to accommodate temperature difference
Wind Stress factor or adjusted wind
U
0 71U
1.23
Wind duratio d uration n (hrs)
W ind in d Waves H in meter, is significant Wave Height Wind Speed
Fetch
W ave ave Height Statisti Statistic c • Hs = H si signifi gnifican cantt , the the av average rage of 33% highe highest st waves waves in the record record • H10 = the average of 10% highest waves in the record Ratio between wave heights and H33 dan H100. Hn/H33