Geology Reference
In-Depth Information
Table 3.
Model results for the case of a gently sloping carbonate ramp:
H
b
is the wave height when the wave breaks,
h
b
is the water depth at which the wave
breaks,
h
t
is the depth where sediment begins to move (
u
>
u
t
), and
u
max
is the maxi-
mum orbital velocity obtained on the ramp prior to the wave breaking. See Table 1
for the other parameter defi nitions.
u
10
(m s
1
)
u
max
(m s
1
)
H
0
(m)
T
p
(s)
H
b
(m)
h
b
(m)
h
t
(m)
6
0.42
2.93
0.38
1.00
1.75
0.54
12
0.98
3.89
0.90
1.99
4.12
0.78
18
1.61
4.59
1.45
3.28
6.55
0.86
34
3.51
5.96
3.11
7.30
12.37
0.80
transport during surge retraction. Since the point
of the model is to explore the effects of storm
waves on a sedimentary system, the model calcu-
lates the bottom orbital velocities for the shoaled
waves through linear wave theory. For each point
along the bathymetric profi le, the bottom orbital
velocity (
u
) is calculated by
(12)
(13)
(
H
b
is the critical wave height at which point the
wave breaks,
(14)
(9)
is the deep water wave length and
S
is the bottom
slope), the wave breaks, the wave height is set to
0.00 m, the bottom orbital velocity is set to 0.0 m s
1
,
and the waves do not regenerate in this model.
To determine the effects of the waves on the
sediments, the bottom orbital velocity was com-
pared to the threshold velocity (
u
t
) for entrain-
ment of sediment of which 50% of the grains have
a diameter smaller than
d
50
.
Application to a carbonate ramp
⎛
⎜
⎞
⎟
r
r
u
=
8
g
s
−
1
d
,
(10)
To investigate the physical potential of laterally
extensive storm deposits that have been inter-
preted in the stratigraphic record, the wave model
was fi rst run for a gently sloping ramp (Fig. 6a).
Table 3 and Fig. 7 provide the results of these
calculations.
For the tropical storms, the waves can break in
3.90 m of water, while the category 1 hurricane can
produce breaking waves in 8.21 m of water depth
which move the sediments beginning in depths of
12.37 m prior to breaking. For these stronger storms
in the real world, the waves lose energy to white cap-
ping and non-linear interactions, so the cases illus-
trated in Fig. 7 represent waves larger than would
actually occur. The depths of infl uence, therefore,
are also larger than should be expected. Overall,
with the modelled waves from the peak of the wave
frequency spectrum, the maximum depth of impact
on a ramp occurs during a Category 1 Hurricane.
In these conditions, the waves can begin to move
bare sediments in 12.37 m of water (these depths
include the surge values, so this depth corresponds
to a depth of 10.87 m below mean sea level). These
results are consistent with the results of detailed
t
50
w
where
r
w
are the densities of the sediment
and water, respectively. In the model, the thresh-
old velocity for sediment entrainment of sedi-
ments of 0.5 mm in diameter (approximately the
average size of the Abaco tidal delta sands) with
an average density of 2.75 g cm
3
(Incze, 1998) is
0.26 m s
1
. This velocity, however, is calculated
for bare sand. If the bottom contains seagrass or
is partially cohesive due to algae or cementation,
the threshold velocity could be much higher. The
depths at which sediment transport begins are
therefore most probably smaller than those calcu-
lated with
u
t
= 0.26 m s
1
.
As the wave steepness increases through
shoaling, it can reach a point where the wave
breaks. To determine the wave height at the point
where it breaks as well as the depth of the water
when the wave breaks, the model includes a
breaker criterion (Kaminsky & Kraus, 1993). Once
a wave exceeds the breaking condition
r
s
and
(11)
