4 Wave generation PRT - LTH · Wind-Generated Waves. 2 Wind Speed -Input for Wave Calculations ......
Transcript of 4 Wave generation PRT - LTH · Wind-Generated Waves. 2 Wind Speed -Input for Wave Calculations ......
2
Wind Speed - Input for Wave Calculations
Correction factors for wind measurements:
• gage elevation
• duration
• temperature
• gage location
Wind Speed Profile in the Lower Atmosphere
1/ 710
(10) ( )U U zz
Velocity profile:
(z = 10 m is the reference height)
(3-26)
Fig. 3-11
Wind Measurement Duration
(10)DU R U
Fig. 3-13
3
5 min: u300/u3600 = 1.13
30 min: u1800/u3600 = 1.02
u3600 = u300/1.13
u1800 = 1.02 * u3600 = 1.02 * u300/1.13 =
Example:
GIVEN: During 5 min a mean wind speed was measured of 10 m/sec.
FIND: The expected mean wind speed representative for 30 min.
= 0.9 * u300 = 0.9 * 10 = 9.0 m/s
Air-Sea Temperature Difference
(10)TU R U
If temperature measurements do not exist, RT = 1.1 should be assumed.
Fig. 3-14
(3-27)
Location of Wind Gage
Ratio between wind speed over water and wind speed over land.
Fig. 3-15
UL
UW=RL*UL
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Wind Input for Wave Calculations
Correction factors for wind measurements:
• gage elevation, RZ
• duration, RD
• temperature, RT
• gage location, RL
Effective wind speed: 1.230.71AU U
meas Z D T LU U R R R R
(3-28a)
Example of Fetch Length
Fetch-limited
Duration-limited
U (m/sec)
2-
2-
5
Nomogram to Determine Significant Wave Height and Peak Spectral Period
Deep Water:
1. Select effectivewind speed (UA = 22 m/s)
2. Indicate wind duration (3 hrs)
3. Indicate fetch length (50 km)
Duration-limited wave conditions! Fig. 3-23
Ch
eck
full
y d
evel
op
ed!
= Hmo = Hs
= Tm
Ts = 0.95 Tm
Hs = 1.9 m Tp = 5.4 sec
U = 22 m/s
tD = 3 hrs Fe = 50 km
Nomogram to Determine Significant Wave Height and Peak Spectral Period
1. Select effectivewind speed (UA = 20 m/s)
2. Indicate wind duration (6 hrs)
3. Indicate fetch length (50 km)
Fetch-limited wave conditions!
Example 1: UA = 20 m/s, tD = 6 hrs, Fe = 50 km. Hs = ?, Tm = ?
Hs = 2.25 mTm = 6.3 sec
Ch
eck
full
y d
evel
op
ed!
6
1. Select effectivewind speed (UA = 20 m/s)
2. Indicate wind duration (6 hrs)
3. Indicate fetch length (150 km)
Duration-limited wave conditions!
Example 2: UA = 20 m/s, tD = 6 hrs, Fe = 150 km. Hs = ?, Tm = ?
Hs = 2.7 mTm = 7.3 sec
Ch
eck
full
y d
evel
op
ed!
Varying Wind SpeedExample 3: Fe = 150 km. UA = 20 m/s 0-4 hrs.
Increasing to 24 m/s 4-8 hrs
After 8 hrs Hs = ?, Tm = ?
0
4
8
12
16
20
24
UA (
m/s
)
0 2 4 6 8Time (hrs)
Actual wind
Assumed wind
●
Example 3a Step 1: UA = 20 m/s, tD = 6 hrs, Fe = 150 km = Example 2
Hs = 2.7 mTm = 7.3 sec
?●
0
4
8
12
16
20
24
UA (
m/s
)
0 2 4 6 8Time (hrs)
Actual wind
Assumed wind
●●
7
●
?●
20
24
150 km
0
4
8
12
16
20
24
UA (
m/s
)
0 2 4 6 8Time (hrs)
Actual wind
Assumed wind
Governing principle: 20 24 ,E E 2 2 2 21
8E gH L H L H T
2 2 2 2 2 2
20 242.7 7.3 388.5H T H T 2 2 2 2
242.85 6.95H T
●●
H2T2 H2T2
Step 2: From UA = 20 m/s to UA = 24 m/s
●
●
20
24
150 km
0
4
8
12
16
20
24
UA (
m/s
)
0 2 4 6 8Time (hrs)
Actual wind
Assumed wind
'
'
'
2.85 m
6.95 s
4.6 hrs
s
m
D
H
T
t
●●
tD’
Step 2: From UA = 20 m/s to UA = 24 m/s
●
●
20
24
150 km
0
4
8
12
16
20
24
UA (
m/s
)
0 2 4 6 8Time (hrs)
Actual wind
Assumed wind
●●
+2 hrs
●
+2 hrs
+2 hrs
3.8 m
8.3 s
6.6 hrs
s
m
D
H
T
t
●
tD’ tD
'
'
'
2.85 m
6.95 s
4.6 hrs
s
m
D
H
T
t
0.95 7.9 ss mT T
Step 3: UA = 24 m/s + 2 hrs
8
0
4 1/25.112 10 m AH u F
2 1/36.238 10 ( ) m AT u F
1/32
32.15
A
Ft
u
0
4 1/25.112 10 m A eH u F
2 1/36.238 10 ( ) m A eT u F
3 3/ 32.15e aF u t
0( , )m mSmallest H T
Fetch Limited Duration Limited
Analytic SMB Wave Calculation
Table 3-2, p 3-48F = 50 km F = 150 kmFeFe
Shallow Water:
Nomogram to Determine
Significant Wave Height and Peak Spectral Period
Fig. 3-27
If shallow water: Use figs for shallow water PLUS fig 3-23 for deep water. Use the SMALLEST H and T!