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problem from a nonlinear perspective (Anderson, 1990;
Yizhaq, Balmorth and Provenzale, 2004) or by using a
complex systems approach employing aspects of emer-
gent behaviour and self-organisation in cellular automa-
ton models (Werner and Gillespie, 1993; Anderson and
Bunas, 1993; Baas, 2002, 2007; Pelletier, 2009).
Bagnold (1941) recognised three categories of ripples:
normal
or
ballistic
;
granule
,
sand ridge
or
mega
; and
fluid drag
or
aerodynamic
. They generally form transverse
to the wind direction in repeated patterns that continu-
ally adjust in response to variability in windflow. Ripples
commonly have wavelengths of 1-25 cm and heights of
0.5-1.0 cm (Sharp, 1963) with a asymmetrical profile con-
sisting of windward slopes of about 10
◦
(Mabbutt, 1977).
However, megaripples can achieve crest-to-crest wave-
lengths exceeding 20 m, are characterised by a bimodal
distribution of coarse and fine particle sizes (Yizhaq
et al.
,
2008) and tend to be more symmetrical in profile (Gree-
ley and Iversen, 1985). This symmetry may be related
to shifts in wind direction, suggesting that the form and
spacing of larger ripples are less dynamic. However, cel-
lular automaton models of ripple formation also suggest
that grain size has a fundamental control on ripple geom-
etry (Anderson and Bunas, 1993; Baas, 2007). Theoreti-
cal and empirical studies by Ellwood, Evans and Wilson
(1975) led to the conclusion that mega- and normal rip-
ples do not form distinct populations, but are the upper and
lower bounds of a continuum in wavelengths as a result
of differences in grain size (Ellwood, Evans and Wilson,
1975) and wind speed, with wavelength responding posi-
tively to increases in both controls (Sharp, 1963; Claudin
and Andreotti, 2006; Andreotti, Claudin and Pouliquen,
2006).
18.7.1
Ballistic ripples
Bagnold's (1941) impact mechanism theory has been
widely used to explain ripple formation. In this theory rip-
ple wavelength is related to a characteristic or mean salta-
tion path length. Surface irregularities act as erosional and
depositional nuclei for moving particles (Figure 18.21).
The windward side of an irregularity is bombarded by
more saltating grains per unit area than the sheltered lee
(a)
Wind direction
B
A
C
Rising limb of
saltation paths
Descending limb of
saltation paths
(b)
Wind direction
Crestal accumulation
of coarser grains
Veneer of
finer grains
10
°
30
°
Core of
finer grains
Foreset bed
