Convectons, anticonvectons and multiconvectons in binary fluid convection

Abstract

Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. Numerical continuation is used to compute such states in the presence of both Neumann boundary conditions and no-slip no-flux boundary conditions in the horizontal. In addition to the previously identified convectons, new states referred to as anticonvectons with a void in the centre of the domain, and wall-attached convectons attached to one or other wall are identified. Bound states of convectons and anticonvectons called multiconvecton states are also computed. All these states are located in the so-called snaking or pinning region in the Rayleigh number and may be stable. The results are compared with existing results with periodic boundary conditions.

Modulated patterns in a reduced model of a transitional shear flow

“…Had they connected their connection would have given rise to a branch starting from the saddle-node of the periodic states, spending some time around Re = 220, before extending monotonically to large Reynolds numbers and resulting in solutions consisting of a spatially modulated roll pattern with a simple structure. Similar modulated states that do not snake but instead extend monotonically to large parameter values have been found in Marangoni convection [1] and studied in detail in the context of binary fluid convection [20]. These studies, in conjunction with earlier studies of model equations such as the Swift-Hohenberg equation [7,9], indicate that in finite domains the behavior of branches of modulated structures is strongly affected by the spanwise spatial period imposed on the system, suggesting that for a different choice of this period homoclinic snaking may in fact be present in the reduced shear flow model studied here.…”

Nonsnaking doubly diffusive convectons and the twist instability

“…This is as expected since the no-slip boundaries destroy the two-dimensional state. 18,20 The same process is repeated for the second type of convecton, the localized twisted states that are produced in tertiary bifurcations from the two-dimensional localized states. Once again, with no-slip boundary conditions the localized states change continuously into extended domain-filling states once they reach the size of the domain, again with defects at the walls.…”

“…[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.…”

Spatial localization in heterogeneous systems

“…8-) peak solution is reached but then doubles back and starts to snake towards states with a lower L 2 norm. As it does so, a defect is created that flattens the central region creating a state reminiscent of a two-pulse state [5,24]. The resulting behavior resembles that of localized structures in SH23 on nonperiodic domains with mixed boundary conditions [25,26].…”

“…These include different convective systems driven by an imposed temperature difference [1][2][3][4][5][6][7], a ferrofluid subject to an imposed magnetic field [8] and an optical light valve experiment driven by a nominally uniform light intensity [9]. Other systems exhibiting localized structures include shear flows [10,11], gas discharges [12], and a variety of optical configurations [13,14].…”