Numerical simulation of binary convection within the Soret regime in a tilted cylinder

Abstract This study computationally investigates the time-dependent patterns emerging in the Soret regime for binary fluid convection in slightly inclined cylinders heated from below, with a particular focus on positive Soret coefficient thermophobic mixtures ( S T &gt; 0) and aspect ratios Γ = 5.2, Γ = 5.3, and Γ = 5.4. By varying the Rayleigh number ( Ra ) and smoothly adjusting its increments, we capture a range of spatio-temporal behaviours, revealing the coexistence of large-scale shear flows (LSF) and superhighway convection (SHC) patterns. SHC-like structures, characterised by a high base frequency, involve oscillating plumes arranged in adjacent lanes, moving in opposite directions along the inclination. Remarkably, this frequency remains nearly constant across different Ra values. Some of the observed coherent structures, such as periodic and modulated solutions, exhibit equivariance with respect to some elements of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msub> <m:mrow> <m:mi mathvariant="double-struck">D</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:math> ${\mathbb{D}}_{2}$ symmetry group inherent to the physical system. In the case of Γ = 5.4, we identify three-frequency orbits, with modulations up to two orders of magnitude smaller than the base frequency. The observed dynamics is highly sensitive to small variations of Γ, with different patterns being stabilized depending on the aspect ratio of the cell. The bifurcation scenarios are complex and case-specific, and their precise determination is computationally demanding.