Flow state multiplicity in convection

Hof, Björn; Lucas, P.; Mullin, T.

doi:10.1063/1.870178

Cited by 44 publications

(44 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As these ranges were given by Wanschura et al only for Pr = 1, a future direction would be to determine the whole zone in the parameter space where the Hopf bifurcation occurs. It would be interesting also to examine more closely the pulsing pattern found by Hof et al (1999) at Ra = 33 000, Γ = 2, Pr = 6.7, in order to determine whether this state, evolving from axisymmetric flow, is the result of a bifurcation similar to that described in the present paper.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

Boronska¹,

Tuckerman²

2006

J. Fluid Mech.

View full text Add to dashboard Cite

The Boussinesq equations for Rayleigh-Bénard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to timedependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25 000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry.

show abstract

Section: Resultsmentioning

confidence: 99%

“…An interesting experimental study was carried out by Hof, Lucas & Mullin (1999). Varying the Rayleigh number through different sequences of values, for fixed parameters Γ = 2.0 and Pr = 6.7, they obtained several different stable patterns for the same final Rayleigh number.…”

Section: Introductionmentioning

confidence: 99%

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

Boronska¹,

Tuckerman²

2006

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…8. In the so-called Rayleigh-Bénard geometry, the multiplicity of states in circular and elliptical domains has been studied by Hof et al 9 and Meevasana and Ahlers, 10 respectively, and one may expect a similar richness in problems without midplane symmetry of which Marangoni convection is typical.…”

Section: Introductionmentioning

confidence: 89%

Nonlinear Marangoni convection in circular and elliptical cylinders

2007

View full text Add to dashboard Cite

OATAO is an open access repository that collects the work of some Toulouse researchers and makes it freely available over the web where possible. The spatial organization of single-fluid Marangoni convection in vertical cylinders with circular or elliptical horizontal cross section is described. The convection is driven by an imposed heat flux from above through Marangoni stresses at a free but undeformed surface due to temperaturedependent surface tension. The solutions and their stability characteristics are obtained using branch-following techniques together with direct numerical simulations. The changes in the observed patterns with increasing ellipticity are emphasized. In some cases, the deformation of the cylinder results in the presence of oscillations.

show abstract

“…For onecomponent fluids, convective patterns including multi-roll patterns, targets and spirals had been obtained in moderate aspect ratio cells by Rüdiger and Feudel (2000), Leong (2002), Ma et al (2006) and Mercader et al (2010). Also, in a series of works motivated by the experimental results obtained by Hof et al (1999), Tuckerman (2010a, 2010b) carried out simulations in a small aspect ratio cell, and a wide variety of steady and time-dependent flows was obtained in the vicinity of the onset of convection. A recent work by Hébert et al (2010) includes some experimental observations on pattern formation near the onset in an intermediate aspect ratio cell and a comparison with some numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Pattern selection near the onset of convection in binary mixtures in cylindrical cells

Alonso

Mercader²,

Batiste

2014

Fluid Dyn. Res.

View full text Add to dashboard Cite

We report numerical investigations of three-dimensional pattern formation of binary mixtures in a vertical cylindrical container heated from below. Negative separation ratio mixtures, for which the onset of convection occurs via a subcritical Hopf bifurcation, are considered. We focus on the dynamics in the neighbourhood of the initial oscillatory instability and analyze the spatiotemporal properties of the patterns for different values of the aspect ratio of the cell, Γ ≲ ≲ 0.25 11 (Γ ≡ R d, where R is the radius of the cell and d its height). Despite the oscillatory nature of the primary instability, for highly constrained geometries, Γ ≲ 2.5, only pure thermal stationary modes are selected after long transients. As the aspect ratio of the cell increases, for intermediate aspect ratio cells such as Γ = 3, multistability and coexistence of stationary and time-dependent patterns is observed. In highly extended cylinders, Γ ≈ 11, the dynamics near the onset is completely different from the pure fluid case, and a startling diversity of confined patterns is observed. Many of these patterns are consistent with experimental observations. Remarkably, though, we have obtained persistent large amplitude highly localized states not reported previously.

show abstract

Flow state multiplicity in convection

Cited by 44 publications

References 10 publications

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

Nonlinear Marangoni convection in circular and elliptical cylinders

Pattern selection near the onset of convection in binary mixtures in cylindrical cells

Contact Info

Product

Resources

About