Oscillatory doubly diffusive convection in a finite container

Landsberg, Adam S.; Knobloch, Edgar

doi:10.1103/physreve.53.3601

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…In an accompanying paper [37] we compute explicitly the normal form coefficients A, B, C in Eqs. (24a,b) for a doubly diffusive system in Hele-Shaw geometry, recently studied in Ref.…”

Section: Fig 16 (Continued)mentioning

confidence: 99%

Oscillatory bifurcation with broken translation symmetry

Landsberg

Knobloch

1996

Phys. Rev. E

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The effect of distant end walls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that.it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L --+ 00 is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations that result take the form of a Hopf bifurcation with approximate D4 symmetry. These equations are able to describe, qualitatively, not only traveling and "blinking" states, but also asymmetrical blinking states and "repeated transients," all of which have been observed in binary fluid convection experiments. PACS number(s): 47.20. Bp, 47.20.Ky, 03.40.Kf

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“…In an accompanying paper [37] we compute explicitly the normal form coefficients A, B, C in Eqs. (24a,b) for a doubly diffusive system in Hele-Shaw geometry, recently studied in Ref.…”

Section: Fig 16 (Continued)mentioning

confidence: 99%

Oscillatory bifurcation with broken translation symmetry

Landsberg

Knobloch

1996

Phys. Rev. E

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“…These equations are of exactly the same form as Eqs. ( 2a) and (2b) by Landsberg and Knobloch (1996b).…”

Section: The Case Of Hopf Onsetmentioning

confidence: 99%

A note on bifurcation problems in large containers

Renardy

1999

Fluid Dyn. Res.

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Recent work has shown that the analysis of bifurcation problems on a large, but ÿnite, interval can yield Landau coe cients which are radically di erent from those obtained for the problem on an inÿnite interval. At ÿrst sight, such results seem to challenge the widely held belief that the onset of instability in a large domain should be described by a Ginzburg-Landau-type amplitude equation. In this note, we show that indeed the same phenomenon can occur when the Ginzburg-Landau equation is used as a starting point. An analysis based on neglecting the spatial derivative terms in the Ginzburg-Landau equation is justiÿable only if the amplitude of the solution is large relative to 1=L, where L is the length of the interval. If the amplitude is small relative to 1=L, then the e ect of the boundary conditions is felt throughout the interval.

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Mode Interactions in Large Aspect Ratio Convection

Hirschberg

Knobloch

1997

J. Nonlinear Sci.

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Oscillatory doubly diffusive convection in a finite container

Cited by 5 publications

References 19 publications

Oscillatory bifurcation with broken translation symmetry

Oscillatory bifurcation with broken translation symmetry

A note on bifurcation problems in large containers

Mode Interactions in Large Aspect Ratio Convection

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