Convectons and secondary snaking in three-dimensional natural doubly diffusive convection

Beaume, Cédric; Bergeon, Alain; Knobloch, Edgar

doi:10.1063/1.4792711

Cited by 38 publications

(50 citation statements)

References 45 publications

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“…Similar bifurcations are present in a vertically extended domain 23 and reflect the presence of a related three-dimensional instability present in small domains with no-slip boundary conditions, as described in Ref. 31.…”

Section: Discussionmentioning

confidence: 78%

“…Both L − 0 and L + 0 undergo snaking between Ra ≈ 1363 and Ra ≈ 1374 before turning supercritical and hence are similar to the secondary snaking branches described in Ref. 23. Figure 6 shows the L 0 solution at bifurcation (lowest panels) followed by the solutions L ∓ 0 at successive saddle-nodes in the snaking region.…”

Section: Closed Containermentioning

confidence: 86%

“…The physical parameters used in the present study are the same as in Ref. 23 and it is therefore of interest to compare the two systems. The domain used in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…The equations are solved for the same parameters as used in Ref. 23, viz., Pr = 1 and τ = 1/11. To allow localized solutions to develop in the domain we choose a large aspect ratio domain, L = 21.…”

Section: -4mentioning

confidence: 99%

“…21,22 Solutions of this type, hereafter referred to as convectons, may be viewed as homoclinic orbits in space connecting the conduction state to itself and are associated with heteroclinic orbits or fronts connecting the conduction state to a periodic roll state and back again. These solutions have recently been computed in natural three-dimensional (3D) doubly diffusive convection in a vertically extended cavity 23 and are accompanied by secondary instabilities leading to the twisting of some of the convection rolls, an instability only allowed by the additional freedom provided by the third dimension. The present paper examines the same system, but this time focusing on a horizontally extended cavity.…”

Section: Introductionmentioning

confidence: 99%

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Nonsnaking doubly diffusive convectons and the twist instability

2013

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Doubly diffusive convection in a three-dimensional horizontally extended domain with a square cross section in the vertical is considered. The fluid motion is driven by horizontal temperature and concentration differences in the transverse direction. When the buoyancy ratio N = −1 and the Rayleigh number is increased the conduction state loses stability to a subcritical, almost two-dimensional roll structure localized in the longitudinal direction. This structure exhibits abrupt growth in length near a particular value of the Rayleigh number but does not snake. Prior to this filling transition the structure becomes unstable to a secondary twist instability generating a pair of stationary, spatially localized zigzag states. In contrast to the primary branch these states snake as they grow in extent and eventually fill the whole domain. The origin of the twist instability and the properties of the resulting localized structures are investigated for both periodic and no-slip boundary conditions in the extended direction. C 2013 AIP Publishing LLC. [http://dx

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Section: Discussionmentioning

confidence: 78%

Section: Closed Containermentioning

confidence: 86%

“…The physical parameters used in the present study are the same as in Ref. 23 and it is therefore of interest to compare the two systems. The domain used in Ref.…”

Section: Discussionmentioning

confidence: 99%

Section: -4mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonsnaking doubly diffusive convectons and the twist instability

2013

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Time-Periodic Forcing of Spatially Localized Structures

Gandhi

Beaume

Knobloch

2015

Springer Proceedings in Physics

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We study localized states in the Swift-Hohenberg equation when timeperiodic parametric forcing is introduced. The presence of a time-dependent forcing introduces a new characteristic time which creates a series of resonances with the depinning time of the fronts bounding the localized pattern. The organization of these resonances in parameter space can be understood using appropriate asymptotics. A number of distinct canard trajectories involved in the observed transitions are constructed.

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