Environmental Engineering Reference
In-Depth Information
6
Noise-induced patterns in environmental systems
6.1 Introduction
A number of environmental processes exhibit the tendency to develop highly orga-
nized geometrical features generally referred to as
patterns
. For example, in arid and
semiarid landscapes the vegetation cover is often sparse and exhibits spectacular orga-
nized spatial features (e.g.,
Macfadyen
,
1950
) that can be either spatially periodic or
random. These patterns exhibit amazing regular configurations of vegetation stripes
or spots separated by bare-ground areas. In some cases patterns may spread over rel-
atively large areas (up to several square kilometers) (
White
,
1971
;
Eddy et al.
,
1999
;
Valentin et al.
,
1999
;
Esteban and Fairen
,
2006
), and can be found on different soils
and with a broad variety of vegetation species and life-forms (i.e., grasses, shrubs, or
trees) (
Worral
,
1959
,
1960
;
White
,
1969
,
1971
;
Bernd
,
1978
;
Mabbutt and Fanning
,
1987
;
Montana
,
1992
;
Lefever and Lejeune
,
1997
;
Bergkamp et al.
,
1999
;
Dunkerley
and Brown
,
1999
;
Eddy et al.
,
1999
;
Valentin et al.
,
1999
).
Because vegetation patterns are observed even when topography and soils do
not exhibit relevant heterogeneity, their formation represents an intriguing case of
self-organized biological systems, which results from completely intrinsic dynamics
(
Lejeune et al.
,
1999
). Self-organization has been also observed in a number of
atmospheric and geomorphic processes. Notable examples include the dynamics un-
derlying the formation of ordered systems of clouds (e.g.,
Krueger and Fritz
,
1961
),
dunes and ripples (e.g.,
Elbelrhiti et al.
,
2005
;
Colombini and Stocchino
,
2008
;
Sem-
inara
,
2010
;
Fourriere et al.
,
2010
), frost boils (
Gleason et al.
,
1986
;
Krantz
,
1990
),
river meandering (e.g.,
Ikeda and Parker
,
1989
), sinuous coastlines (
Ashton et al.
,
2001
), or fringed peatlands (e.g.,
Eppinga et al.
,
2008
). In all of these cases spatial
self-organization has been explained as the result of
symmetry-breaking instability
,
which leads to the emergence of stable heterogeneous configurations.
To investigate these processes scientists capitalized on the understanding
of pattern-forming mechanisms gained in other fields, such as fluid dynamics
240
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