The fate of self-aligned rolls in gravity modulated magnetoconvection

We explore the modifications brought about by gravity modulation in self-aligned two-dimensional (2D) stationary rolls and higher-order convective instabilities with horizontal magnetic field. The Chandrasekhar number plays no role in determining critical values of the forcing parameters for convection to begin. The onset is in the form of 2D rolls with periodically varying intensity. The external magnetic field is solely responsible for aligning the rolls while the induced magnetic field comes into play after three-dimensional convection sets in. Gravity modulation destabilizes the system and results in chaotic flow much earlier above onset.     

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.     

Chaotic travelling rolls in Rayleigh-Bénard convection

In this paper we investigate two-dimensional (2D) Rayleigh-Bénard convection using direct numerical simulation in Boussinesq fluids with Prandtl number P = 6.8 confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number r (770 < r < 890) the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.     

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non-Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg–Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the coupling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.     

Different localized states of travelling-wave convection in a rectangular container

We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendicular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and supercritical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable. The weak structures in the conducting region are demonstrated too.     

Thermal convection currents in NMR: flow profiles and implications for coherence pathway selection

Rayleigh-Benard convection currents are visualized in a vertical cylindrical tube by means of magnetic resonance imaging. Axially antisymmetric flow, multiple vertical rolls, and twisted node planes are observed. The flow can also be induced by strong RF irradiation. Its effects on the coherence pathways in NMR experiments employing field gradients are discussed. Copyright 2000 Academic Press.     

Convection in horizontally vibrated granular material

We report observations of convective motion in a container filled with granular material when it is vibrated in the horizontal direction. We find that the roughness of the boundaries and the container dimensions play an important role in determining the shape and number of the convection cells. When the container bottom and lateral walls are rough, the system typically exhibits four counter-rotating rolls stacked in two pairs on top of each other; for very low filling height, it is possible to observe a single row of rolls arranged laterally along the bottom of the container. With smooth walls, on the other hand, we find that the system typically forms only a single pair of counter-rotating convection rolls that originate in the two upper corners of the vibrated material; when the filling height is increased to a level that depends on the container width, we observe a transition to the four-roll state. (c) 1999 American Institute of Physics.     

Dynamics of zero-Prandtl number convection near onset

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Be?nard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.     

Temperature dependence of the critical magnetic field of the structural transition in MBBA-based ferronematics

We studied the structural transitions in ferronematics based on the thermotropic nematic liquid crystal MBBA (4^′ -methoxybenzylidene-4-n-butylaniline) having a nematic-to-isotropic transition temperature T _N–I?=?48.0^○C and in MBBA-based ferronematics doped with a magnetic suspension consisting of Fe₃O₄ particles (10?nm in diameter) coated with oleic acid as a surfactant. The ferronematic samples were prepared with different volume concentrations of magnetic particles φ?=,1× 10^?4, 2× 10^?4 and 5×10^?4. The temperature dependences of the critical magnetic fields in a bias electric field under strong applied magnetic fields are presented. We calculated the surface density of anchoring energy W at the nematic–magnetic particle boundary. Scaling of the structural transition in the MBBA and MBBA-based ferronematics with the temperature of the nematic-to-isotropic transition was observed.     

Magnetic field-induced orientational phases of ferronematics in shear flow

We examine the effect of shear flow on the orientational phase transitions induced by a magnetic field in ferronematic liquid crystals. Continuum approach based on the generalized Leslie–Ericksen theory is used to describe the dynamics of ferronematic liquid crystals. We consider three orientations of the magnetic field in a plane of shear flow. Stationary solutions for the director and the magnetization are obtained as functions of the magnetic field strength for different values of material parameters. Our results show that shear flow can lead to the shift of the field thresholds or to a “smoothing” of the magnetic field-induced transitions in ferronematics. In the limiting case of pure nematic liquid crystals, we revealed threshold effects, which are unstipulated by the orientational elasticity of a liquid crystal, in contrast to the conventional Fréedericksz transition.     

Elastic convection in vibrated viscoplastic fluids

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.     

Oscillations, cessations, and circulation reversals of granular convection in a densely filled rotating container

We study spontaneously forming convection in a container that is almost completely filled with a bidisperse granular mixture. The container with an aspect ratio close to 1 rotates slowly about a horizontal axis. In this geometry, single vortex rolls are observed in the cell plane, after a spontaneous symmetry breaking. The circulation of grains produces nonuniform segregation patterns of the mixture that in turn interact with the convective flow. We describe oscillatory modulations of the convection velocity, cessations and spontaneous reversals of the circulation. All these features are absent in multiroll granular convection.     

Benard-Marangoni convection in two-layered liquids

We describe experiments on Benard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.     

Wall-enhanced convection in vibrofluidized granular systems

An event-driven molecular dynamics simulation of inelastic hard spheres contained in a cylinder and subject to strong vibration reproduces accurately experimental results [R. D. Wildman et al., Phys. Rev. Lett. 86, 3304 (2001)] for a system of vibrofluidized glass beads. In particular, we are able to obtain the velocity field and the density and temperature profiles observed experimentally. In addition, we show that the appearance of convection rolls is strongly influenced by the value of the sidewall-particle restitution coefficient. Suggestions for observing more complex convection patterns are proposed.     

竖壁传热对方腔内Benard对流的影响

本文采用具有QUICK差分格式的SIMPLE算法对边界竖壁传热的方腔内空气Benard对流进行了数值计算,根据计算结果探讨了竖壁传热对Benard对流的影响.计算表明,在所考虑的几何和物理条件下,所有竖壁绝热时,腔内流体形成平行与短轴的多个涡卷;竖壁存在传热时,腔内流体形成平行于长轴的两个涡卷,并且平行于长轴竖壁的传热热流方向相反时,涡卷的旋转方向也相反;垂直于长轴蛏壁的传热对近壁附近的流动有一定影响.     

Order and fluctuations in nonequilibrium molecular dynamics simulations of two-dimensional fluids

Finite systems of hard disks placed in a temperature gradient and in an external constant field have been studied, simulating a fluid heated from below. We used the methods of nonequilibrium molecular dynamics. The goal was to observe the onset of convection in the fluid. Systems of more than 5000 particles have been considered and the choice of parameters has been made in order to have a Rayleigh number larger than the critical one calculated from the hydrodynamic equations. The appearance of rolls and the large fluctuations in the velocity field are the main features of these simulations.     

Convection in highly fluidized three-dimensional granular beds

Free, buoyancy-driven convection has been observed experimentally in three-dimensional highly fluidized granular flows for the first time. Positron emission particle tracking was used to determine the position of a tracer grain in a vibrofluidized bed, from which packing fraction distributions as well as the velocity fields could be determined. The convection rolls, although small compared to the magnitude of velocity fluctuations (<5%), were consistently observed for a range of grain numbers and shaker amplitudes. Density variations are a signature of free convection and, with negative temperature gradients also present, were interpreted as the mechanism by which the convection rolls were initiated.     

Effect of electric and magnetic fields on the orientation structure of a ferronematic liquid crystal

We analyze uniform orientation phases in soft ferronematics (suspensions of magnetic nanoparticles in nematic liquid crystals) induced by electric and magnetic fields. It is shown that the competition between the electric and magnetic fields can lead to various sequences of orientation transitions in a ferronematic depending on the energy of coupling between the director and magnetization. We obtain and analyze phase diagrams of these transitions. A sequence of re-entrant transitions in the orientation structure (angular phase-homeotropic phase-angular phase-planar phase) is predicted for a certain range of the coupling energies and electric field strengths.