Geometric diagnostics of complex patterns: Spiral defect chaos

Riecke, Hermann and Sánchez Madruga, Santiago (2006). Geometric diagnostics of complex patterns: Spiral defect chaos. "Chaos", v. 16 ; pp.. ISSN 1054-1500. https://doi.org/10.1063/1.2171515.

Description

Title: Geometric diagnostics of complex patterns: Spiral defect chaos
Author/s:
  • Riecke, Hermann
  • Sánchez Madruga, Santiago
Item Type: Article
Título de Revista/Publicación: Chaos
Date: 2006
ISSN: 1054-1500
Volume: 16
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

More information

Item ID: 21710
DC Identifier: http://oa.upm.es/21710/
OAI Identifier: oai:oa.upm.es:21710
DOI: 10.1063/1.2171515
Official URL: http://chaos.aip.org/chaos/copyright.jsp
Deposited by: Memoria Investigacion
Deposited on: 22 Nov 2013 10:25
Last Modified: 21 Apr 2016 12:26
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