Standing-Wave Oscillations in Binary Mixture Convection: From the Onset via Symmetry Breaking to Period Doubling into Chaos

Abstract

Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients psi. Galerkin as well as finite-difference simulations were used. They were augmented by simple control methods to obtain also unstable SW states. For sufficiently negative psi, unstable SWs bifurcate subcritically out of the quiescent conductive state. They become stable via a saddle-node bifurcation when lateral phase pinning is exerted. Eventually their invariance under timeshift by half a period combined with reflection at midheight of the fluid layer gets broken. Thereafter, they terminate by undergoing a period-doubling cascade into chaos.

Collisions of localized convection structures in binary fluid mixtures

“…In fact, the buoyancy difference between regions with different concentrations has already been identified in [11] as the cause of the traveling convection waves. However, the oscillatory behavior [3,6,8,9,[12][13][14][15][16][17][18][19][20][21][22] appears not only in the form of spatially extended, fully relaxed, nonlinear TW convection, but also in TW fronts moving into the quiescent fluid. Also, a mostly unstable standing wave solution branches out of the conductive state at the common Hopf bifurcation threshold.…”

Thermal convection in mixtures with an inversion of the separation ratio

“…Qualitative changes that happen at or close to ψ = 0 are for example the appearance of a bifurcation threshold for heating from above when ψ < 0, the appearance of a Hopf bifurcation threshold, also when ψ < 0, and the change of the stationary bifurcation for R > 0 from a forward type (for ψ > 0) to a backward type (for ψ < 0). As a consequence of these changes, convection at small Rayleigh numbers is dominated by stationary structures like roll and square patterns for positive ψ [9][10][11][12][13][14][15], whereas for ψ < 0 oscillatory structures like traveling and standing waves bifurcate first [16][17][18][19][20][21][22][23].…”

Oscillatory convection in binary mixtures: Thermodiffusion, solutal buoyancy, and advection

“…In this section we compare characteristic properties of spatially extended oscillatory convection in the form of relaxed TWs [19,30,31], SWs [16] and of oscillatory transients [15] into, say, a nonlinear TW. In Fig.…”