Simulations of oscillatory convection in He3–He4 mixtures in moderate aspect ratio containers

Abstract

Simulations of 3 He-4 He mixtures with negative separation ratios in two-dimensional containers with realistic boundary conditions and moderately large aspect ratio ⌫ are described. The system exhibits a large variety of states with complex time dependence including intermittent wave localization and chaotic "repeated transients." Steady but localized states are also found. Particular attention is paid to the transitions that occur for ͑R − R c ͒ / R c Ϸ ⌫ −2 , where R is the Rayleigh number and R c its critical value for the primary instability, in order to clarify the gradual transition from a small number of active degrees of freedom ͓͑R − R c ͒ / R c Ӷ⌫ −2 ͔ to many active degrees of freedom ͓͑R − R c ͒ / R c ӷ⌫ −2 ͔.

Homoclinic snaking of localized states in doubly diffusive convection

“…The structures identified differ from the dispersive chaos 19 present close to Ra H and represent spatially localized but chaotic traveling waves. Similar waves have been seen in direct numerical simulations in a closed large-aspect-ratio two-dimensional container at larger supercriticality 42 and resemble the traveling wave packets observed in experiments. 43 In periodic domains, these nonlinear wave packets drift in the direction of the phase velocity (s 0 > 0, as confirmed below) but much more slowly.…”

Convectons, anticonvectons and multiconvectons in binary fluid convection

“…It is therefore of great interest to examine in greater detail the properties of 'real' systems such as convection or shear flows in order to identify gaps in our understanding of the properties of these states, and to suggest extensions of the theory to realistic situations. In the present paper, we focus on spatially localized steady convection in binary mixtures with negative separation ratio heated from below (Batiste & Knobloch 2005a;Batiste et al 2006), and follow Blanchflower (1999) in referring to such states as convectons to distinguish them from other localized states found in binary fluid convection such as localized travelling waves (Kolodner, Surko & Williams 1989;Steinberg et al 1989;Barten et al 1995;Batiste & Knobloch 2005b).…”

Localized structures in convective experiments

“…Specifically, the time-independent binary fluid system studied in [47,52] is equivariant under the spatial reflection R: (x) to (−x), where (x) is the horizontal coordinate, and hence is reversible as dynamical system in space, i.e. (x) acts as time-like variable [14][15][16]42,[46][47][48][49][50][51][52][53][54][55][56].…”

“…Localized traveling rolls have been shown in experiments of convection in nematic liquid crystals under electric fields [10], in cryogenic 3He-4He binary mixtures and even in pure fluids with inhomogeneous heating [11]. Also has been studied numerically in magnetofluids (where the name "convecton" appear for the first time) [12,13], in 3He-4He mixtures [14,15], and in Marangoni convection (surface tension driven) in binary fluids [16], but the number of new successful experiments reported up today is very low.…”