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Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection

Published online by Cambridge University Press:  28 September 2012

Takeshi Watanabe ,
Makoto Iima  and
Yasumasa Nishiura
Takeshi Watanabe*
Affiliation:
Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, 1-7-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8521, Japan
Makoto Iima
Affiliation:
Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, 1-7-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8521, Japan
Yasumasa Nishiura
Affiliation:
WPI Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
*
†Email address for correspondence: [email protected]
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Abstract

We study spontaneous pattern formation and its asymptotic behaviour in binary fluid flow driven by a temperature gradient. When the conductive state is unstable and the size of the domain is large enough, finitely many spatially localized time-periodic travelling pulses (PTPs), each containing a certain number of convection cells, are generated spontaneously in the conductive state and are finally arranged at non-uniform intervals while moving in the same direction. We found that the role of PTP solutions and their strong interactions (collision) are important in characterizing the asymptotic state. Detailed investigations of pulse–pulse interactions showed the differences in asymptotic behaviour between that in a finite but large domain and in an infinite domain.

JFM classification

Instability: Absolute/convective instability Nonlinear Dynamical Systems: Bifurcation Convection: Double diffusive convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 219 - 243
Copyright
©2012 Cambridge University Press

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