EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
(3) If dimensionless wave frequency (defined simply as one over the spectral peak wave period) defined
as
u( fp
f^p '
(II-2-25)
g
where
fp = frequency of the spectral peak
then a stationary wave field also implies a fixed relationship between wave frequency and fetch of the form
^m
f^p ' λ2 X 2
(II-2-26)
where
λ2 and m2 are more empirical coefficients.
(4) Since u* scales the effective rate of momentum transfer from the atmosphere into the waves, all
empirical coefficients in these wave generation laws are expected to be universal values. Unfortunately, there
is still some ambiguity in these values; however, in lieu of any demonstrated improvements over values from
the Shore Protection Manual (1984), those values for fetch-limited wave growth will be adopted here.
(5) From basic conservation laws and the dispersion relationship, it is anticipated that any law governing
the rate of growth of waves along a fetch will also form a unique constraint on the rate of growth of waves
through time. If we define dimensionless time as
gt
t^ '
(II-2-27)
u(
where
t = time
additional relationships governing the duration-growth of waves will be
m
^
H ' λ3 t^ 3
(II-2-28)
and
m
f^p ' λ4 t^ 4
(II-2-29)
where
λ4 and m4 are more "universal" coefficients to be determined empirically.
(6) The form of Equations II-2-26 and II-2-27 imply that waves will continue to grow as long as fetch
and time continue to increase. This concept was observed to be incorrect in the early compendiums of data
II-2-38
Meteorology and Wave Climate
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