Oscillatory binary fluid convection in large aspect-ratio containers

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.     

Numerical simulations of binary fluid convection in large aspect ratio annular containers

The patterns arising in large aspect ratio annular containers heated from below are analyzed for water-ethanol mixtures with negative Soret coupling. The subcritical Hopf bifurcation at the onset of convection leads to a very rich dynamics. Using high resolution numerical tools based on spectral methods to solve the hydrodynamic equations we obtain and review the properties of the different regimes arising in early stages of convection: spatially extended stationary and travelling wave convective roll structures, dispersive chaotic states, and several types of localized convection. The dynamics triggered by the Eckhaus–Benjamin–Feir instability is presented for a mixture with a moderate negative value of the separation ratio.     

Unstable periodic solution controlling collision of localized convection cells in binary fluid mixture

We study the collision processes of spatially localized convection cells (pulses) in a binary fluid mixture by the extended complex Ginzburg-Landau equations. Both counter- and co-propagating pulse collisions are examined numerically. For counter-propagating pulse collision, we found a special class of unstable time-periodic solutions that play a critical role in determining the output after collision. The solution profile right after collision becomes close to such an unstable pattern and then evolves along one of the unstable manifolds before reaching a final destination. The origin of such a class of unstable solutions, called scattors, can be traced back to two-peak bound states which are stable in an appropriate parameter regime. They are destabilized, as the parameter is varied, and become scattors which play the role of separators of different dynamic regimes. Delayed feedback control is useful to detect them. Also, there is another regime where the origin of the scattors is different from that of the above case. For co-propagating pulse collision, it is revealed that the result of pulse collision depends on the phase difference between pulses. Moreover, we found that a coalescent pulse keeps a profile of two-peak bound state, which is not observed in the case of counter-propagating pulse collision. Complicated collision dynamics become transparent to some extent from the viewpoint of those unstable objects.     

Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong soret effect

Spatially confined solutions of traveling convection rolls are determined numerically for binary mixtures such as ethanol-water. The appropriate field equations are solved in a vertical cross section of the rolls perpendicular to their axes subject to realistic horizontal boundary conditions. The localized convective states are stably and robustly sustained by strongly nonlinear mixing and complex flow-induced concentration redistribution. We elucidate how this enables their existence for strongly negative separation ratios at small subcritical heating rates below the saddle node of extended traveling convection rolls where the quiescent fluid is strongly stable.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

On the brink of jamming: granular convection in densely filled containers

Granulates are ubiquitous in nature and technology, but, despite their great importance, their dynamics are by far less well understood than those of liquids. We demonstrate in an almost compactly filled flat (Hele-Shaw) cell, where slow horizontal rotation simulates a variable gravitational force, that unexpected dynamic structures may arise under geometrical restrictions. The cell motion drives regular flow in the compact interior, and convection rolls combine with segregation. The container fill level is crucial for the dynamic regime. A transition from chute flow at lower fill levels to convection in densely packed containers is found. These observations suggest the existence of comparable phenomena in situations where so far no systematic search for dynamic patterns has been performed.     

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil...     

Sloping convection in a rotating fluid

Laboratory experiments on thermal convection in a fluid which rotates about a vertical axis and is subject to a horizontal temperature gradient show that when the rotation rate Ω exceeds a certain critical value Ω_R (which depends on the acceleration of gravity, the shape and dimensions of the apparatus, the physical properties of the fluid and the distribution and intensity of the applied differential heating) Coriolis forces inhibit overturning motion in meridian planes and promote a completely different type of flow which has been termed ‘sloping convection’ or ‘baroclinic waves’. The motion is then non-axisymmetric and largely confined to meandering ‘jet streams’, with trajectories of individual fluid elements inclined at only very small (though essentially non-zero) angles to the horizontal. The kinetic energy of the waves derives from the interaction of slight vertical motions with the potential energy field maintained by differential heating, and it is dissipated by friction arising largely in boundary layers on the walls of the apparatus.

Provided that Ω, though greater than Ω_R, does not exceed a second critical value Ω_I, the waves are characterized by great regularity; they are either steady or undergo periodic ‘vacillation’ in their amplitude, shape and other properties. The azimuthal wavelength decreases with increasing Ω until at Ω=Ω_I it reaches a sufficiently low value, ～1.5 times the radial dimension of the wave, for nonlinear processes to overcome various constraints associated with the anisotropy of the flow, thereby rendering the main baroclinic wave barotropically unstable by transferring kinetic energy to larger as well as smaller scales of motions.

Theoretical investigations of sloping convection have their origin in ideas concerning the large-scale mid-latitude circulation of the Earth's atmosphere, modern work on which includes important studies based on numerical models. Conditions favouring sloping convection should be fairly common in natural systems and the process is expected to underlie various phenomena of interest to oceanographers, geophysicists, planetary scientists and astronomers.     

Vibrational convection of a binary mixture in connected channels

The influence of high-frequency vibrations on the thermal convection of a binary mixture in connected channels is investigated theoretically. The oscillatory and stationary convective flows are calculated using the finite difference method in combination with the Galerkin procedure. Numerical simulation has revealed that the vertical vibrations substantially affect the threshold of convection and different characteristics of the supercritical regimes.