EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
II-2-2. Wave Hindcasting and Forecasting
a.
Introduction.
(1) The theory of wave generation has had a long and rich history. Beginning with some of the classic
works of Kelvin (1887) and Helmholtz (1888) in the 1800's, many scientists, engineers, and mathematicians
have addressed various forms of water wave motions and interactions with the wind. In the early 1900's, the
work of Jeffreys (1924, 1925) hypothesized that waves created a "sheltering effect" and hence created a
positive feedback mechanism for transfer of momentum into the wave field from the wind. However, it was
not until World War II that organized wave predictions began in earnest. During the 1940's, large bodies of
wave observations were collated and the bases for empirical wave predictions were formulated. Sverdrup
and Munk (1947, 1951) presented the first documented relationships among various wave-generation
parameters and resulting wave conditions. Bretschneider (1952) revised these relationships based on
additional evidence; methods derived from these exemplary pioneer works are still in active use today.
(2) The basic tenet of the empirical prediction method is that interrelationships among dimensionless
wave parameters will be governed by universal laws. Perhaps the most fundamental of these laws is the
fetch-growth law. Given a constant wind speed and direction over a fixed fetch, it is expected that waves will
reach a stationary fetch-limited state of development. In this situation, wave heights will remain constant (in
a statistical sense) through time but will vary along the fetch. If dimensionless wave height is taken as
gH
^
H'
(II-2-22)
2
u(
where
H = characteristic wave height, originally taken as the significant wave height but more recently taken
as the energy-based wave height Hm0
and dimensionless fetch is defined as
gX
^
X'
(II-2-23)
2
u(
where
X = straight line distance over which the wind blows
then idealized, fetch-limited wave heights are expected to follow a relationship of the form
^m
^
H ' λ1 X 1
(II-2-24)
where
λ1 = dimensionless coefficient
m1 = dimensionless exponent
Meteorology and Wave Climate
II-2-37
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