Convectons in periodic and bounded domains

Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar

doi:10.1088/0169-5983/42/2/025505

Cited by 18 publications

(36 citation statements)

References 20 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The origin and properties of these states are now well established Mercader et al 2010). In particular, it is known that when the system possesses reflection symmetry in the midplane (i.e.…”

mentioning

confidence: 99%

Travelling convectons in binary fluid convection

et al. 2013

Self Cite

View full text Add to dashboard Cite

Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd-and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton's law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift-Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.

show abstract

mentioning

confidence: 99%

Travelling convectons in binary fluid convection

et al. 2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…Observe that the pinning regions of the odd and even states are now noticeably different although their left boundaries coincide. This is a consequence of horizontal pumping of concentration by the odd parity states, as explained in [25,26]. Note also that both pinning regions are broader, a fact that can be attributed to the more negative value of S. This change in S promotes subcriticality of the periodic branch P 7 .…”

Section: 2mentioning

confidence: 83%

“…Our continuation results broaden significantly the parameter space in which spatially localized states are known to be present [5]. A different set of parameter values was used in two recent studies of convectons in closed twodimensional containers [25,26].…”

mentioning

confidence: 93%

See 1 more Smart Citation

Dissipative solitons in binary fluid convection

Mercader¹,

Batiste²,

Alonso³

et al. 2011

Discrete &Amp; Continuous Dynamical Systems - S

Self Cite

View full text Add to dashboard Cite

Abstract.A horizontal layer containing a miscible mixture of two fluids can produce dissipative solitons when heated from below. The physics of the system is described, and dissipative solitons are computed using numerical continuation for three distinct sets of experimentally realizable parameter values. The stability of the solutions is investigated using direct numerical integration in time and related to the stability properties of the competing periodic state.1. Introduction. Many fluid systems exhibit spatially localized structures in both two [2,4,5,7,9,14,16] and three [10,23] dimensions. Of these the localized structures or convectons arising in binary fluid convection are perhaps the best studied. These states are similar to localized structures studied in other areas of physics [1] despite the fact that fluid systems must always be confined between boundaries. On the other hand in fluid systems the length scale is typically set by the layer depth or the distance between any confining boundaries instead of being an intrinsic length scale selected by a Turing or modulational instability. As a result when we speak of localized states in binary fluid convection we mean states that are localized in the horizontal direction only. In this sense the problem resembles laser systems in short cavities in which the standing wave structure in the longitudinal direction remains of paramount importance [15].In fluids dissipation, whether through viscosity or thermal diffusion, is generally of great importance. For example, it is responsible for the presence of a finite threshold value of the Rayleigh number, a dimensionless measure of thermal forcing, for convection to occur. As a result the solitons of interest in the present article are strongly dissipative and hence require strong forcing for their maintenance. States of this type cannot therefore be understood in terms of (an infinite-dimensional) Hamiltonian system with small forcing and dissipation.In this paper we study localized states in binary fluid convection in a horizontal layer of depth h heated from below. Binary liquids, such as water-ethanol and watersalt mixtures or mixtures of He 3 -He 4 at cryogenic temperatures, are characterized by a cross-diffusion effect called the Soret effect that describes the diffusive separation

show abstract

“…[14][15][16] Recent work has focused on spatially localized convection first observed by Ghorayeb and Mojtabi 17 in natural doubly diffusive convection. Since then stationary localized convection has been extensively studied in two-dimensional (2D) doubly diffusive convection in a horizontal layer, both with Soret effect [18][19][20] and without. 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.…”

Section: Introductionmentioning

confidence: 99%

Nonsnaking doubly diffusive convectons and the twist instability

2013

Self Cite

View full text Add to dashboard Cite

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

show abstract

Convectons in periodic and bounded domains

Cited by 18 publications

References 20 publications

Travelling convectons in binary fluid convection

Travelling convectons in binary fluid convection

Dissipative solitons in binary fluid convection

Nonsnaking doubly diffusive convectons and the twist instability

Contact Info

Product

Resources

About