Geoscience Reference
In-Depth Information
pre-transport environment of the boulder were developed (Nott, 2003). These
equations relate four forces; drag, lift, inertia and restraint, incorporating the
effect of buoyancy, acting upon a boulder of given shape to the velocity of the
breaking wave. Expressed mathematically, the first three forces must exceed or
equal the force of restraint in order to initiate transport of a boulder (involving
overturning), such that
F
d
+
F
l
+
F
m
≥
F
r
(5.3)
Where:
F
d
(drag force moment)
={
0
.
5ρ
w
C
d
(
ac
)
u
2
}
c
/
2
(5.4)
F
l
(lift force moment)
={
0
.
5 ρ
w
C
l
(
bc
)
u
2
}
b
/
2
(5.5)
F
m
(intertia force)
=
ρ
w
C
m
(
abc
)
u
(5.6)
F
r
(restraining force moment)
=
(ρ
s
−
ρ
w
)(
abc
)
gb
/
2
(5.7)
density of water at 1.02 g ml
−
1
, ρ
s
density of boulder at 2.4 g cm
−
3
,
with ρ
w
=
=
C
d
=
coefficient of drag
=
2,
C
l
=
coefficient of lift
=
0.178,
g
=
gravitational
constant,
ü
=
instantaneous flow acceleration,
u
=
flow velocity/bore celerity,
a
C
axis of boulder.
Combining these forces together, as expressed in equation (5.3), and incor-
porating the velocity for storm waves at breaking point as
gh
0.5
and tsunami as
2
gh
,gives three different equations depending upon the pre-transport setting of
the boulder. For submerged (submarine) boulders where,
=
A
axis of boulder,
b
=
B
axis of boulder,
c
=
F
d
+
F
l
≥
F
r
(5.8)
The equation relating wave height to boulder size for tsunami is
H
t
≥
0
.
25 (ρ
s
−
ρ
w
)
/
ρ
w
2a
/
[
C
d
(
ac
/
b
2
)
+
C
l
]
(5.9)
where
H
t
=
height of tsunami, and, for storm waves
(ρ
s
−
ρ
w
)
/
ρ
w
2a
/
[
C
d
(
ac
/
b
2
)
+
C
l
]
H
s
≥
(5.10)
where
H
s
=
height of storm wave at breaking point.
Forsubaerial boulders (where the boulder is exposed on dry land such as a
shore platform) inertia force must be incorporated into an equation to describe
theimpact of a wave upon that boulder; in a submerged position the boulder
is buttressed by the water and the inertia force is absorbed by the boulder. A
subaerial boulder will be transported when,
F
d
+
F
l
≥
F
r
−
F
m
(5.11)
Search WWH ::
Custom Search