268 Gerbrand J. Komen
Conventional and satellite observations are complementary. Satellites have a global coverage, which is agreat advantage, but their repeat cycle (the time lapse
between two observations at the same position) is rather low. Conventional observations, on the other hand, have excellent temporal resolution, but they are point
measurements, so their spatial coverage is restricted by the number of instruments
one has.
Fig. 14.1 shows a scatter plot in which for a large number of cases the wave
height is given as a function of the wind speed. (The cases are model simulations
rather than observations, but they are sufficiently realistic to be used as an illustration of the point.) It is important to note that there is no clear relationship. The solid
line is an attempt to draw a relation I . But as you can see, it fails. At low wind
speed waves are higher than expected. These are cases in which advection of
energy (swell) is important. At high wind speed most wave heights lie below the
curve. This is because they are not yet fully grown.
To illustrate this we will discuss wave generation in a number of simple situations.
14.2.1 Duration- and fetch-limited wave growth
Imagine an infinite flat windless ocean. At a given time, say t = O, a uniform
wind starts blowing. Due to instability (Kawai, 1979) waves begin to form. They
grow with time. The significant wave height Hs, everywhere equal, will be a simple function of two variables, the wind speed u and time t:
Hs = Hs(u, t)
(1)
Wind-generated surface waves are gravity waves, i.e. waves in which gravity is
the restoring force. Therefore, one may expect that their behaviour scales with the
strength ofthe gravitational acceleration g. This allows one to rewrite ( 1 ) as
Hs _ {t g )
-g -
- ,
u 2
U
(2)
where f is a function that has been determined from observations. Wave modellers
can not agree on the exact shape of fbut typically Hs g/i grows as a function of
tg/u to reach a maximum level of Hs g/u 2 = 0.22 at tg/u = 2 X 10 5 . (For longer
durations the growth becomes negligible, i.e. at tg/u = 2 x 10 5 when the wave
height reaches its asymptotic value the waves are fully grown, and can't grow
higher for that given wind speed.) For a typical (strong) wind of 20 mls, it takes
1. This particular curve is a parametrisation proposed by Sanders in the 1970s for
the maximum significant wave height that would be reached under steady wind
conditions (H s max = ~ U 2 10 / g, with a mean winter value for ~ of 0.22, as
opposed to the summer value which was only 0.14 (Janssen, Komen and de
Voogt, 1984».
Conventional and satellite observations are complementary. Satellites have a global coverage, which is agreat advantage, but their repeat cycle (the time lapse
between two observations at the same position) is rather low. Conventional observations, on the other hand, have excellent temporal resolution, but they are point
measurements, so their spatial coverage is restricted by the number of instruments
one has.
Fig. 14.1 shows a scatter plot in which for a large number of cases the wave
height is given as a function of the wind speed. (The cases are model simulations
rather than observations, but they are sufficiently realistic to be used as an illustration of the point.) It is important to note that there is no clear relationship. The solid
line is an attempt to draw a relation I . But as you can see, it fails. At low wind
speed waves are higher than expected. These are cases in which advection of
energy (swell) is important. At high wind speed most wave heights lie below the
curve. This is because they are not yet fully grown.
To illustrate this we will discuss wave generation in a number of simple situations.
14.2.1 Duration- and fetch-limited wave growth
Imagine an infinite flat windless ocean. At a given time, say t = O, a uniform
wind starts blowing. Due to instability (Kawai, 1979) waves begin to form. They
grow with time. The significant wave height Hs, everywhere equal, will be a simple function of two variables, the wind speed u and time t:
Hs = Hs(u, t)
(1)
Wind-generated surface waves are gravity waves, i.e. waves in which gravity is
the restoring force. Therefore, one may expect that their behaviour scales with the
strength ofthe gravitational acceleration g. This allows one to rewrite ( 1 ) as
Hs _ {t g )
-g -
- ,
u 2
U
(2)
where f is a function that has been determined from observations. Wave modellers
can not agree on the exact shape of fbut typically Hs g/i grows as a function of
tg/u to reach a maximum level of Hs g/u 2 = 0.22 at tg/u = 2 X 10 5 . (For longer
durations the growth becomes negligible, i.e. at tg/u = 2 x 10 5 when the wave
height reaches its asymptotic value the waves are fully grown, and can't grow
higher for that given wind speed.) For a typical (strong) wind of 20 mls, it takes
1. This particular curve is a parametrisation proposed by Sanders in the 1970s for
the maximum significant wave height that would be reached under steady wind
conditions (H s max = ~ U 2 10 / g, with a mean winter value for ~ of 0.22, as
opposed to the summer value which was only 0.14 (Janssen, Komen and de
Voogt, 1984».