Geology Reference
In-Depth Information
where
f
c
is a botto
m
friction coefficient, determined
experimentally, and
u
= depth-averaged current velocity.
Equation
2.3
describes the so-called “quadratic friction
law”, i.e., the friction exerted by a fluid flow is pro-
portional to its velocity squared. Equations
2.1
-
2.3
suggest that the faster the flow velocity and the rougher
the bed, the greater the shear stress, and therefore the
greater potential of sediment transport.
Although wave forcing is not the dominant factor in
determining the overall morphology and sedimentation
pattern in tidal environments, it is important in local
sediment entrainment and transport. For example,
numerous studies have shown that wave forcing can
have significant influence on the sedimentology and
morphodynamics of tidal flats (Christie et al.
1999
;
Dyer
1998
; Dyer et al.
2000
; Li et al.
2000
; Talke and
Stacey
2003, 2008
; Lee et al.
2004
). Wave motion can
be visualized as a circular motion of an imaginary
water particle. This wave orbital velocity, especially
near the bottom, can induce considerable shear stress
to entrain and transport sediment. Based on linear
wave theory, the maximum value of near bottom orbital
velocity (
U
G
) is:
with wave breaking tends to be much greater than that
under non-breaking waves and a typical current.
Various empirical formulas were developed to evaluate
“when” waves break (Kaminsky and Kraus
1994
),
one of the simplest and also reasonably accurate
formulas is:
H
0.78
h
(2.6)
b
b
where
H
b
= breaking wave height,
h
b
= water depth at
which waves break. In other words, waves break when
their height is about 80% of the water depth. Wells and
Kemp (
1986
) found that muddy bottoms, typical of
some tidal environments, can dissipate wave energy
to such an extent that the above breaking criterion is
never reached. Although wave forcing is secondary in
tidal environments, it can contribute significantly to
local sediment transport, especially in the nearshore
region and during storm conditions, and should not be
neglected.
In addition to the basic hydrodynamic parameters
described in Eqs.
2.1
-
2.6
, sediment grain size (
D
) and
density (U
s
) also play a crucial part in understanding
and estimating sediment entrainment and transport.
Mean grain size (
d
m
) and the 50th percentile size (
d
50
)
are typically used to represent natural sediment that is
composed of grains with a range of sizes. The ratio of
the fluid force and the submerged particle weight yields
probably the most commonly used dimensionless
parameter, the Shields parameter (T), in quantifying
sediment entrainment and transport:
p
H
U
(2.4)
d
2
p
h
¤
¥
¦ µ
T
sinh
L
where
h
= water
depth,
L
= wave
length,
T
= wave
period, and
H
= wave height.
In a more simplified larger scale approach, wave-
induced sediment transport is often evaluated based on
the amount of energy that is carried by the wave.
Higher wave energy typically results in more active
sediment transport. Wave energy per unit water
volume (
E
) is determined as:
2
*
t
q
rr
u
b
(2.7)
(
)
gD
(
s
1)
gD
s
w
where
D
= grain diameter, and
s
= sediment specific
density = U
s
/U
w
.
Settling velocity (
w
s
) is another key parameter,
especially for suspended sediment transport. Under
most circumstances, the settling velocity of sediment
particles is defined as the terminal velocity through
tranquil water. Therefore, it is regarded as one of the
physical properties of sediment particle and is not
related to the flow regime, although actual settling
velocity through turbulent water can be very different
from that through tranquil water. Numerous studies
have been conducted on particle settling resulting in
the development of a variety of empirical formulas.
For particles that are smaller than fine sand, Stoke's
1
8
(2.5)
2
E
r
gH
w
Equation
2.5
shows that wave energy is proportional to
wave height squared, e.g., a 2 m wave will carry four
times the energy than a 1 m wave.
Waves break as they propagate from deep water
into shallow water. The energy that is carried by the
wave motion is dissipated rapidly through wave break-
ing. A large portion of this energy is expended to
transport sediment. Due to the intense turbulence gen-
erated by wave breaking, sediment transport associated
