Effect of small inclination on binary convection in elongated rectangular cells

Abstract

We analyze the effect of a small inclination on the well-studied problem of two-dimensional binary fluid convection in a horizontally extended closed rectangular box with a negative separation ratio, heated from below. The horizontal component of gravity generates a shear flow that replaces the motionless conduction state when inclination is not present. This large scale flow interacts with the convective currents resulting from the vertical component of gravity. For very small inclinations the primary bifurcation of this flow is a Hopf bifurcation that gives rise to chevrons and blinking states similar to those obtained with no inclination. For larger but still small inclinations this bifurcation disappears and is superseded by a fold bifurcation of the large scale flow. The convecton branches, i.e., branches of spatially localized states consisting of counterrotating rolls, are strongly affected, with the snaking bifurcation diagram present in the non-inclined system destroyed already at small inclinations. For slightly larger but still small inclinations we obtain small amplitude localized states consisting of corotating rolls that evolve continuously when the primary large scale flow is continued in the Rayleigh number. These localized states lie on a solution branch with very complex behavior strongly dependent on the values of the system parameters. In addition, several disconnected branches connecting solutions in the form of corotating rolls, counterrotating rolls, and mixed corotating and counterrotating states are also obtained.

Inclined convection in a layer of liquid water with poorly conducting boundaries

“…A notable exception to this behavior occurs in binary liquid mixtures, where even an inclination of the sample as small as few milliradians strongly affects the convective planform [18][19][20][21][22]. This feature of binary mixtures can be qualitatively understood by taking into account that in the case of solutal convection the boundaries are impermeable.…”

“…A convective square planform has been reported also for solutal convection in a binary liquid mixture, where the impermeable boundaries are formally analog to perfectly insulating boundaries in the thermal case. So far, the influence of inclination on pattern formation with impermeable or poorly conducting boundaries has been investigated mostly in binary liquid mixtures [18][19][20]22], but not in single component fluids with poorly conducting boundaries.…”

Traveling-Wave Convection with Periodic Source Defects in Binary Fluid Mixtures with Strong Soret Effect

“…Laboratory experiments have observed convective states taking the form of traveling waves (TW) [ 2 ], localized TW (LTW) [ 3 , 4 ], stationary overturning convection (SOC) [ 2 ], blinking [ 5 , 6 ], counterpropagating waves (CPW, or “chevrons”) [ 7 , 8 ], repeated transients [ 7 , 8 ] and dispersive chaos [ 9 ]. After these pioneering studies, many research by direct numerical simulations (DNS) were conducted to further understand and identify the mechanisms of the convective states, see e.g., References [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. By DNS one can get easily the values at any point of the flow fields and extract from them information difficult or impossible to obtain in the experiments, this allows a better understanding of the convective states.…”

“…For low Rayleigh numbers, it is also challenging to investigate the problem by 3D simulations for a broad range of control parameters. Two-dimensional (2D) simulation, which is substantially less computational cost and found to capture many essential features of 3D convection [ 30 , 31 ], is a useful tool in fundamental research and has been widely used to study Rayleigh–Bénard convection, not only in binary fluids [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] but also in one-component fluid [ 28 , 29 , 32 , 33 ]. Barten and his coworkers [ 10 ] first reported the DNS results of convection in water-ethanol mixtures with separation ratio , and then studied in detail the TW and SOC states in binary mixtures with different values in a narrow container of a single wavelength [ 11 ].…”

“…We studied convection in binary mixtures with a weak separation ratio of , observed a undulation TW and five stable SOC states with different mean wavenumber (Here n is the number of roll pairs) in the container with the aspect ratio of , and also discussed in detail the influence of fluid parameters and aspect ratio on the onset of convection and the properties of the five new stable SOC states [ 21 ]. Mercader and coworkers [ 22 ] analyzed the effect of a small inclination of angles and on the 2D binary fluid convection with a negative separation ratio .…”