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and longer is its saltating jump. The manner of momentum
extraction from the airflow is demonstrated by the wind
tunnel experiments of Rasmussen and Sørensen (2008),
who recorded 1:1 ratios between air and grain speed within
80 mm of the surface, increasing to a ratio of 2.0 at 5
mm height. Grain size also has an influence on trajec-
tory paths, with larger grains rebounding from the surface
at lower speeds and following a shorter and lower tra-
jectory (Namikas, 2003). Similarly, Willetts (1983) noted
that grain shape influences the trajectory with platy grains
tending to have lower and longer paths than spherical
grains. The length of jump is thought to be of the order of
12-15 times the height of bounce (Livingstone and War-
ren, 1996) and the trajectory is also influenced if the grain
starts to spin after a glancing impact. Reports of spin
rates reaching over 400 r.p.s (White and Schultz, 1977;
White, 1982) can induce a lift force (termed the Magnus
effect) that may extend saltation trajectories. Particle col-
lisions with the surface effectively convert near-horizontal
momentum (with angles of descent up to 10
◦
)toaverti-
cal momentum via ejection or rebound. Ungar and Haff
(1987) noted that the number of grains splashed up into
the airstream by an impacting grain was proportional to
the square of the impacting grain velocity, which may be
up to 5 times its initial velocity (Anderson and Hallett,
1986).
The height of the saltation layer is dependent on the
wind speed (Dong
et al.
, 2002), the grain size in transport
and surface characteristics. Bagnold (1941) recognised
that saltation leaps were higher on a pebbly or hard rock
surface than on a loose sand surface because hard sur-
faces are less absorbent of the grain momentum on each
bounce. Pye and Tsoar (1990) quote a maximum salta-
tion height on such surfaces of 3 m, although heights of
∼
Figure 18.20
Saltating sand being swept from the crest of
an 80 m high linear dune in the Namib Desert. Increasing
wind speeds and saltation impacts result in progressively more
intense saltation from dune foot to dune crest (photo: author).
induce mass transport of sediment in a cascading system
(Figure 18.20), often termed the 'fetch effect' (Gillette
et al.
, 1996). A limit to the amount of sediment in salta-
tion is set when an equilibrium is established between the
fluxes of sediment and air as a result of the momentum
extracted from the airflow by the saltating grains. This
momentum extraction causes a considerable reduction in
near-surface wind speeds during saltation (Owen, 1964)
and results in the majority of grain ejections being intiated
by impact from other saltating grains rather than by direct
fluid entrainment.
Bagnold (1936, 1941) was the first to appreciate
the ballistic trajectory of saltating grains and there
are numerous studies that have investigated the sub-
processes of grain entrainment, trajectory, bed colli-
sion and velocity profile modification, principally rely-
ing on wind tunnel and numerical modelling approaches
(e.g. Willetts and Rice, 1986a, Anderson and Hallett,
1986; Werner and Haff, 1988; Anderson and Haff,
1988; Rasmussen and Mikkelsen, 1991; Werner, 1990;
McEwan, Willetts and Rice, 1992; McEwan, 1993; Haff
and Anderson, 1993; Dong
et al.
, 2002; Kok and Renno,
2009b; Namikas, 2003; Rasmussen and Sørensen, 2008;
Bauer, Houser and Nickling, 2004).
Bagnold (1941) and Chepil (1945) both identified steep
initial take-off angles of grains at angles approaching 90
◦
.
However, other studies have recognised a range of lift-
off angles of between 15 and 70
◦
(White and Schultz,
1977; Nalpanis, 1985; Willetts and Rice, 1985a; Ander-
son, 1989; Namikas, 2003; Kok and Renno, 2009b). The
actual grain trajectory depends very much on the height of
bounce of the grain into the boundary layer. Wind speeds
increase at a logarithmic rate away from the surface (see
0.2 m are more commonly found. However, the mass of
saltating particles decreases very rapidly with height and
has been described by a declining exponential function
(Rasmussen, Sørensen and Willetts, 1985; Dong
et al.
,
2002; Rasmussen and Sørensen, 2008), with up to 80 %
of all transport taking place within 2 cm of the surface
(Butterfield, 1991).
18.7
Ripples
The sediment transport mechanisms of creep, reptation
and saltation combine to create ripples, a mobile bed-
form that contributes to bulk sediment transport. Despite
decades of research these features still remain enigmatic
and our understanding of them is incomplete. Wind tunnel
and numerical modelling investigations on the controls on
