Geoscience Reference
In-Depth Information
18.8 Prediction and measurement of
sediment flux
side and so is an area of net erosion. The preferential
loss of particles on the windward side of the emergent
ripple creates a new zone of bombardment downwind, at
a distance equivalent to the mean saltation path length.
Hence, the ripple pattern migrates downwind as a series
of alternating zones of erosion and protection. Coarser
grains, which are not set into saltation by the impact of
bombarding grains, creep forward to accumulate in the
less bombarded crestal zone.
However, Sharp (1963) notes that ripple spacing in-
creases with time and so it is unlikely to be related to
the mean saltation path length under steady wind condi-
tions. In contrast, he suggested that the angle of incidence
of descending particles and ripple height determined rip-
ple spacing. Height can perhaps be seen as crucial; given
the narrow range of ripple slope angles that have been
recorded, it must geometrically affect the length of the
windward and lee slopes. Thus, the minimum wavelength
must increase with height (Brugmans, 1983) and rip-
ple wavelength must increase correspondingly as ripple
growth proceeds. As the ripple protrudes further into the
boundary layer and coarser grains on the crest are more
readily moved forward, the height of the ripple becomes
limited (Greeley and Iversen, 1985).
Wind tunnel and theoretical studies have indicated
how saltation dynamics might influence ripple wave-
lengths. Saltating particles require vertical lift-off momen-
tum while creeping grains require forward momentum.
Willetts and Rice (1986a, 1986b) have calculated that
bombarding grains transfer relatively more vertical energy
on steeper slopes and more horizontal energy on shallower
slopes. Thus, saltation is favoured from the middle of
the windward side of ripples and creep activity increases
towards the crest, favouring the accumulation of coarse
grains (Figure 18.21).
Anderson (1987) has suggested that while ripple wave-
length is affected by grain trajectory lengths, it is not the
same distance as the mean saltation path length. A crit-
icism of Bagnold's (1941) theory was that it relied on a
very narrow range in saltation path lengths, although ex-
perimental studies showed that saltation trajectories were
often widely distributed and variable (Mitha et al. , 1986).
Anderson's (1987) model therefore includes a wide range
of saltation trajectory lengths and speeds that drive a rep-
tating population. In this model ripples are formed through
the accumulation of these reptating grains, with a wave-
length that is a function of the probability distribution of
the total trajectory population and the ejection rate of the
reptating grains. This reptation control of ripple develop-
ment has support from the wind tunnel experiments of
Willets and Rice (1986b) and simulations of Werner and
In order to quantify surface erosion or deposition, geo-
morphologists are often interested in the changing rate
of sediment flux in space and/or time. There are many
equations to calculate mass sand flux from wind velocity
data, nearly all derived from theoretical or wind tunnel
experimental work (see Greeley and Iversen, 1985, for a
review). All the expressions tend to the form of
A u 3
=
q
(18.9)
The two types of relationship frequently used to calcu-
late sand flux are typified by the expressions of Bagnold
(1941) and Kawamura (1951), the latter incorporating a
specific term for the threshold shear velocity for entrain-
ment:
D ) 0 . 5 u 3
q
=
C ( d
/
ρ/
g (Bagnold
,
1941)
(18.10)
u ct ) 2
q
=
K k ( u
u ct )( u
ρ/
g (Kawamura
,
1951)
(18.11)
where
sand transport rate (gm 1
s 1 )
q
=
C
=
constant (1.8 for naturally graded dune sand)
d
=
grain diameter
D
=
standard grain diameter (0.25 mm)
ρ =
air density
K k =
constant (2.78)
u ct =
threshold of grain entrainment
Well-known problems with the Bagnold (1941) expres-
sion include the fact that it predicts sand movement below
the threshold of entrainment and it commonly predicts
rates that are considered too low at high values of shear
velocity (Sarre, 1987). Owing to the inclusion of a thresh-
old term in the Kawamura (1951) calculation, it is more
accurate at lower levels of shear velocity. However, this
Search WWH ::




Custom Search