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
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