Vegetative Flat Dryland Rhombic Pattern Formation Driven by Root Suction

David J. Wollkind () and Bonni J. Dichone
Additional contact information
David J. Wollkind: Washington State University, Department of Mathematics
Bonni J. Dichone: Gonzaga University, Department of Mathematics

Chapter Chapter 18 in Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, 2017, pp 457-487 from Springer

Abstract: Abstract A rhombic planform nonlinear cross-diffusive instability analysis is applied to an interaction-diffusion plant-ground water model system in an arid flat environment containing a root suction effect. A threshold-dependent paradigm is introduced to interpret stable rhombic patterns driven by this plant root suction effect in the ground water equation. The results of that analysis are represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. From those plots regions corresponding to bare ground and vegetative patterns consisting of isolated patches, rhombic arrays of pseudo-spots or -gaps separated by an intermediate rectangular state, and homogeneous distributions from low to high density are identified in this parameter space. Then that morphological sequence, produced upon traversing an experimentally determined root suction characteristic curve, is compared with observational evidence relevant to the occurrence of leopard, pearled, or labyrinthine-type tiger bush, used to motivate an aridity classification scheme, and compared with some recent nonlinear vegetative pattern formation studies. There are four problems: The first two fill in some details of this analysis while the last two examine critical conditions for the onset of instability for a related vegetation model and rhombic pattern formation for an ion-sputtered solid surface erosion model.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-73518-4_18

Ordering information: This item can be ordered from
http://www.springer.com/9783319735184

DOI: 10.1007/978-3-319-73518-4_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().