1

Typical Periods

Wind

Wind-Generated Waves

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

4

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!