Environmental Engineering Reference
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Figure 5.4. Example of meandering river in an arid environment.
Patterns can exhibit a remarkable spatial regularity with the periodic recurrence
in space of some geometrical features, such as circles, stripes, gaps, or labyrinths
(e.g., see Figs. 5.1 , 5.2 ). In these cases, the main sign of the pattern formation is the
occurrence of a dominant wavelength in the field variable. This definition of pattern
based on periodicity is often used in the literature on pattern formation for several
reasons: First, it corresponds to a clearly defined concept of regularity (i.e., existence of
periodicity); second, periodicity is a field property that is easily caught by the eyes and
can be detected by spectral analysis; third, the occurrence of dominant wavelengths
can be studied theoretically by use of established mathematical tools such as stability
analysis by normal modes or the analysis of the structure function (see Subsection ). Although these three reasons explain why pattern and spatial periodicities are
often considered to be the same thing, it is important to stress that sometimes spatial
fields are defined as patterned even when several length scales are present and no clear
Figure 5.5. Example of desert ripples on dunes.
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