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Growth shapes and turbulent spots in unstable systems

Growth shapes and turbulent spots in unstable systems We study the growth shapes of localized turbulent patches (turbulent spots) in a class of partial differential equations (PDEs) in two spatial dimensions, of first order in time and in one scalar field u . The PDE’s are chosen such that the ‘‘laminar’’ state u =0 is unstable, at least convectively (i.e., in a moving frame). We show which symmetry breaking terms are required to generate the characteristic nonconvex growth shapes found in turbulent spots in boundary layers, and how the shapes transform when we vary the coefficients of these terms. Finally, we show how it is possible, in certain cases, to find exact solutions for the nonliear growth shapes and how to measure Lyapunov exponents of growing turbulent spots. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Growth shapes and turbulent spots in unstable systems

Physical Review E , Volume 51 (5) – May 1, 1995
19 pages

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References (15)

Publisher
American Physical Society (APS)
Copyright
Copyright © 1995 The American Physical Society
ISSN
1095-3787
DOI
10.1103/PhysRevE.51.4485
Publisher site
See Article on Publisher Site

Abstract

We study the growth shapes of localized turbulent patches (turbulent spots) in a class of partial differential equations (PDEs) in two spatial dimensions, of first order in time and in one scalar field u . The PDE’s are chosen such that the ‘‘laminar’’ state u =0 is unstable, at least convectively (i.e., in a moving frame). We show which symmetry breaking terms are required to generate the characteristic nonconvex growth shapes found in turbulent spots in boundary layers, and how the shapes transform when we vary the coefficients of these terms. Finally, we show how it is possible, in certain cases, to find exact solutions for the nonliear growth shapes and how to measure Lyapunov exponents of growing turbulent spots.

Journal

Physical Review EAmerican Physical Society (APS)

Published: May 1, 1995

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