EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
where
X = straight line fetch distance over which the wind blows
Hm0 = energy-based significant wave height
CD = drag coefficient
U10 = wind speed at 10 m elevation
u* = friction velocity
See Demirbilek, Bratos, and Thompson (1993) for more details.
Fully developed wave conditions in these equations are given by
g Hm
' 2.115 x 102
(
2
u(
(II-2-37)
and
g Tp
' 2.398 x 102
u(
Equations governing wave growth with wind duration can be obtained by converting duration into an
equivalent fetch given by
3
gX
gt
&3
2
' 5.23 10
(II-2-38)
u(
2
u(
where t in this equation is the wind duration. The fetch estimated from this equation can then be substituted
into the fetch-growth equations to obtain duration-limited estimates of wave height and period.
(c) Narrow fetches. Early wave prediction nomograms included modifications to predicted wave
conditions based on a sort of aspect ratio for a fetch area, based on the ratio of fetch width to fetch length.
Subsequent investigations (Resio and Vincent 1979) suggested that wave conditions in fetch areas were
actually relatively insensitive to the width of a fetch; consequently, it is recommended here that fetch width
not be used to estimate an effective fetch for use in nomograms or the ACES Program. Instead, it is
recommended that the straightline fetch be used to define fetch length for applications.
(d) Shallow water. Many studies suggest that water depth acts to modify wave growth. Bottom friction
and percolation (Putnam 1949, Putnam and Johnson 1949, Bretschneider and Reid 1953) have been
postulated as significant processes that diminish wave heights in shallow water; however, recent studies in
shallow water (Jensen 1993) indicate that fetch-limited wave growth in shallow water appears to follow
growth laws that are quite close to deepwater wave growth for the same wind speeds, up to a point where an
asymptotic depth-dependent wave height is attained. In light of this evidence, it seems prudent to disregard
bottom friction effects on wave growth in shallow water. Also, evidence from Bouws et al. (1985) indicates
that wave spectra in shallow water do not appear to have a noticeable dependence on variations in bottom
sediments. Consequently, it is recommended that deepwater wave growth formulae be used for all depths,
Meteorology and Wave Climate
II-2-45
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