EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
(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
X 0.67
tx , u ' 77.23
(II-2-35)
u 0.34 g 0.33
where
tx,u = time required for waves crossing a fetch of length x under a wind of velocity u to become fetch-
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
g Hm
gX
' 4.13 10&2(
2
0
2
2
u(
u(
and
1
g Tp
gX
3
' 0.651
(II-2-36)
u(
2
u(
2
u(
CD '
2
U10
CD ' 0.001(1.1 % 0.035 U10)
II-2-44
Meteorology and Wave Climate
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