Geology Reference
In-Depth Information
distance over which it has blown (fetch). After a
certain period of time, the waves are no longer time
dependent and become fetch-limited. To ensure that
the waves are past the limit for a duration-limited
sea state and that the fetch-limited equation given
above is adequate for calculating the wave heights,
the model calculates this time limit (
t
d
) using
platform. As waves enter relatively shallow water,
the waves shoal, indicating that the wave height
increases, the wave length (
L
) decreases, and
steepness (ratio of wave height to wave length)
increases. The wave height (
H
) at a given depth
(
h
) is calculated using the equations for wave
shoaling:
(4)
(2)
(5)
The model then assumes the wind has been blow-
ing steady longer than this limit to the duration-
limited sea state. The model then generates waves
from a fetch of 16 km (based on an assumption of a
10-mile scale for daily land or sea breezes). Model
runs with other fetch values (25 and 50 km) yielded
similar results to the 16 km fetch, except the larger
waves produced by a longer fetch broke in deeper
water such as at the platform margin, limiting
the waves that pass over a platform. The calcula-
tions with the 16 km fetch produced waves that
propagated over the platform rather than breaking
at the platform edge, for most wind speeds.
The model calculates the peak wave period for
the given wind conditions using
where
k
s
is the shoaling coeffi cient (relates the
deep water wave height to the wave height at a
given water depth,
h
),
c
is the wave phase velocity
(the speed of individual waves),
c
o
is the deep-
water wave phase velocity
(6)
(7)
and
n
is defi ned as
(8)
(3)
where
h
is the water depth and
k
is the wave
number. For simplicity, the model assumes
shore-perpendicular waves and shore-parallel
depth contours; therefore, wave refraction can
be neglected. Storm surges were incorporated by
adding the average surge estimated by the Tropical
Prediction Center/National Hurricane Center for
each type of storm (Table 2) to the bathymetri-
cal profi le (in the above equations, substitute
(
h
+ surge) for
h
), but the current velocities pro-
duced by a storm surge were not modelled. These
currents, however, may be important to the over-
all impact of the storm and cause downslope
The effects of four different wind conditions
representing the daily trade winds, winter North
Easters, tropical storm winds, and hurricane
(Category 1) strength winds are explored with the
model. Table 1 gives the results of the deep water
wave prediction module.
Wave transformation and breaking
Waves generated in deeper water can propagate
towards the coast (carbonate ramp) or across a
Table 1.
Results of the deep water wave module
computations. This table gives the values of the wind speed
at 10 m above sea level (
u
10
), the wind stress factor (
u
*
),
the deep water signifi cant wave height (
H
0
), the peak
period of the wave spectrum (
T
p
), and the time limit to the
duration-limited sea state (
t
d
).
u
10
(m s
1
)
Table 2.
Wind speed (
u
10
) and surge values used in the
numerical wave model for the different types of winds:
daily winds, storm winds (winter storm), and tropical
cyclones of both Tropical Storm strength and Category 1
Hurricane strength (on the Saffi r-Simpson Scale).
u
*
(m s
1
)
H
0
(m)
T
p
(s)
t
d
(h)
Daily
winds
Storm
winds
Tropical
storm
6
6.43
0.42
2.93
10.5
Category
Category 1
12
15.09
0.98
3.89
14.0
Wind speed (m s
1
)
18
24.89
1.61
4.59
16.6
6
12
18
34
34
54.32
3.51
5.96
21.5
Surge (m)
0.0
0.5
1.0
1.6
