(1) Assumptions in simplified wave predictions.

(a) Deep water. There are three situations in which simplified wave predictions can provide accurate

estimates of wave conditions. The first of these occurs when a wind blows, with essentially constant

direction, over a fetch for sufficient time to achieve steady-state, fetch-limited values. The second idealized

situation occurs when a wind increases very quickly through time in an area removed from any close

boundaries. In this situation, the wave growth can be termed duration-limited. It should be recognized that

this condition is rarely met in nature; consequently, this prediction technique should only be used with great

caution. Open-ocean winds rarely can be categorized in such a manner to permit a simple duration-growth

scenario. The third situation that may be treated via simplified prediction methods is that of a fully developed

wave height. Knowledge of the fully developed wave height can provide valuable upper limits for some

design considerations; however, open-ocean waves rarely attain a limiting wave height for wind speeds above

50 knots or so. Equation II-2-30 provides an easy means to estimate this limiting wave height.

(b) Wave growth with fetch. Figure II-2-3 shows the time required to accomplish fetch-limited wave

development for short fetches. The general equation for this can be derived by combining the JONSWAP

growth law for peak frequency, an equation for the fully developed frequency, and the assumption that a local

wave field propagates at a group velocity approximately equal to 0.85 times the group velocity of the spectral

peak. This factor accounts for both frequency distribution of energy in a JONSWAP spectrum and angular

spreading. This yields

(II-2-35)

where

limited

Equation II-2-35 can be used to determine whether or not waves in a particular situation can be categorized

as fetch-limited.

The equations governing wave growth with fetch are

1

' 4.13 10&2(

2

0

2

2

1

3

' 0.651

(II-2-36)

2

2

2

II-2-44

Meteorology and Wave Climate

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