Convective Roll Pattern Research Articles

Numerical study of free convection in a thin layer between coaxial horizontal cylinders

We consider free convection in 2D and 3D horizontal cylindrical layers with the inner hot and outer cold boundary at Ra (Rayleigh number) in range (4∙103 ÷ 4∙105) and the ratio δ ≈ 1:20 of the layer width to inner radius. Prandtl number was 0,71, fluid properties were taken for air at 293 K.It was shown that the flow in a 2D cylindrical layer can be divided into three regions. Stable symmetric convective rolls are formed in the layer’s upper part; regions with the transient flow appear at the lateral sides; transitional regions between the upper and the lateral regions have convective rolls of an unusual asymmetric shape.The flow in a 3D cylindrical layer in the upper part is organized into a spatially stable convective roll pattern. With increase of the Rayleigh number (Ra), roll pattern becomes suppressed by a transient plume pattern.The global Nu (the Nusselt number) is proportional to 0,0019∙Ra0,567 for the 2D case and to 0,22∙Ra0,192 for the 3D case. The 2D problem provides a reasonable estimation of the Nusselt number for Rayleigh number up to 4∙104 and overestimates Nu for higher Rayleigh number, which agrees with Lyapunov exponent values.

Freely suspended smectic films with in-plane temperature gradients

Freely suspended smectic films with in-plane temperature inhomogeneities can exhibit remarkable thermocapillary (Marangoni) effects. The temperature dependence of the surface tension promotes flow in the film plane, convection roll patterns, and climbing of smectic layers against gravitational forces. We discuss several experimental geometries where macroscopic material transport is driven by temperature gradients, including experiments under normal gravity and observations in microgravitation during suborbital rocket flights and on the International Space Station. In all these experiments, the temperature dependence of the surface tension drives unidirectional material flow. The divergence of this flow near the hot and cold film edges, and at the boundaries of film islands in the film, is associated with the creation, motion and removal of dislocations. These dissipative processes limit the flow velocity.

Responses of spatiotemporal chaos to oscillating forces.

The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, M(p)(t), which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, M(p)(t) oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of M(p)(t) to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of M(p)(t) contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of M(p)(t).

Time reversal of the excitation wave form in a dissipative pattern-forming system

We discuss the consequences of time reversal of the excitation parameters on the stability of a periodically driven dynamic system. The example chosen, electrohydrodynamic convection of nematics, is a well-investigated dissipative pattern-forming system, usually driven with time-periodic external electric fields E(t) . The dynamic model that describes linear stability at onset can be represented by a set of two differential equations for the amplitudes of the dynamic variables. Floquet analysis reveals an astonishing dynamic property: Under time reversal of any periodic excitation function E(t) , the dynamic equations reproduce the same stability thresholds, pattern types, and critical pattern wavelengths, even when the dynamics of all involved system variables are essentially different for the excitations E(t) and E(-t) . Experimental confirmation of these mathematical predictions is provided by the measurement of threshold curves and the analysis of the time-resolved optical characteristics of the convection roll patterns.

Rayleigh–Bénard convection in liquid metal layers under the influence of a horizontal magnetic field

This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.

Convection Flip in the Rayleigh-Bénard Problem in a Small System

Molecular dynamics study of the Rayleigh-Benard system was explored about ten years ago by Mareschal et al. 1), 3) and by Rapaport. 2) The former researchers demonstrated that fully developed convective rolls could be observed even in a small system made up of a few thousands of molecules. In the present study, we focus on an unsteady behavior of convective roll observed near the conventional critical point. Our system consists of 1600 hard disks confined to a square box at a number density of 0.2. The temperatures of the upper and the lower walls are T0(1 − ∆T/2) [K] and T0(1 +∆T/2) [K], respectively, and a gravitational field is introduced so that a disk moving between these two walls experiences a zero net energy change. Initially, the disks are uniformly spaced and their velocities are sampled from the Maxwellian distributions with linearly interpolated temperatures between the two thermal walls. Disks are assumed to be reflected specularly on the walls; however, thermal effect is taken into account to the normal component of the velocity departing from the upper and the lower walls. A series of experiments was performed by changing the value of ∆T from 0.2 to 1.8. The square box is devided into small cells and the variations of local velocity in each of these cells are successively measured by taking an average in an appropriate time scale. General observations are summarized as follows. Spontaneous single-roll structure clearly appears when ∆T > 1; at first, both clockwise and counterclockwise convections are observed irregularly. As ∆T increases, the average lifetime of a convective roll pattern, τroll, is prolonged and finally no flip motion occurs on an observational time scale τobs. We realize that there is a short range of ∆T , instead of a distinct critical point, between no-roll and fully developed single-roll states. To characterize the state in this transitional phase, we introduce two parameters. Let M∗ be the sum of nondimensional angular momentum of all disks around the center of the box. This is, so to speak, an order parameter which describes the transformation from structureless no-roll (disordered) state to fully developed singleroll (ordered) state. Using this, we introduce new parameters M1 and M2 such that

Control parameter in granular convection

We perform dynamic simulations of discrete systems involving convection roll patterns. The present study reveals that the self-diffusion constant $D$ and the energy diffusivity $\ensuremath{\alpha}$ are two transport coefficients relevant to dynamic granular systems. This conforms to the basic physics of vibrated granules: a phenomenon of mass diffusion induced by energy injection. The ratio $D/\ensuremath{\alpha}$ gives rise to an intrinsic physical property which, together with the external vibrational acceleration, constitutes a dimensionless control parameter equivalent to the Rayleigh number in heat induced fluid convection.

Convection Roll Patterns for Fluidized Granules

Convection Roll Patterns for Fluidized Granules

Wavenumber evolution in Rayleigh-Bénard convection with air in moderate size containers

We summarize here the results of wavenumber evolution in Rayleigh-Bénard experiments with air in moderate size rectangular containers. The wavenumber reduction selection mechanism originates from growth of skewed varicose instability, and is facilitated by dynamical motions of dislocation defects in the convection roll pattern. The regime of stable, two-dimensional convection roll patterns in moderate size containers is found to exist, however, at much larger buoyant potential than that observed and predicted in wide horizontal layers. We suggest that this aspect of Rayleigh-Bénard convection in gases derives from a stabilization of the pattern as forced by the modulation effects of all vertical boundaries in the container. The wavenumber evolution reported here accounts for new experimental results, which exhibit two alternative branches in the commencement of the secondary bifurcation structure.

Flow structure transition mechanisms in thermal convection of air in rectangular containers

Transition of convection roll patterns is evaluated empirically for horizontal moderate size containers of air heated below and cooled above. Characteristics of the transitions are of interest in the study of nonlinear dynamical systems, since the regime of convection roll flow structures precedes the appearance of turbulent convection in experiments with increasing buoyancy.

Correlation of subsystems for the transition to a convective pattern

The authors implement an evolutionary model of spatially coupled subsystems to clarify the cooperative effect causing the transition to a convective roll pattern in a Rayleigh-Benard cell. This cell is swept through its threshold by means of a step in the heat input from the lower plate. The correlation of subsystems accounts for the amplification of fluctuations. The experimental transients for the onset of the convective pattern are shown to be theoretically reproducible.

Constraints on the time-reversible Liouville equation in order to derive a stochastic order-parameter equations at the onset of a convective roll pattern

It is shown that an adequate Fokker-Planck equation for the transition to a convective roll pattern in a Rayleigh-Benard cell can be derived by projecting the time-reversible Liouville equation onto the centre manifold for the onset and introducing the source of irreversibility on the initial conditions. Thus the author elucidates the microscopic origin of the random source in the order-parameter evolution.

Transition to a convective roll pattern as obtained from the stochastic center-manifold theory.

We prove that the transition to a convective pattern in a Rayleigh-B\'enard cell with a step in the heat input can be obtained by restricting the system to the locally attractive and locally invariant center manifold in phase space. The problem of providing the adequate scaling factor for the random source in the order-parameter equation is solved and the theoretical findings reproduce satisfactorily the experimentally measured time dependence for the convective heat flow.

Domain Structure in the Nematic Freedericksz Transition

Abstract In the course of experiments using the Freedericksz transition on a planar nematic film in a magnetic field perpendicular to the limiting plates, we have observed the transient existence of a periodic roll structure very similar to published observations by Carr, and apparently similar to Williams domains. The present paper develops a model based on the effect of the decrease of the effective viscosity in the presence of the back flow, induced by the rotation of n and taking place as a convective roll pattern. Direct observations and order of magnitude estimates of the wavelength of the roll and of the time constant for the development of the rolls agree with the model. We also addressed ourselves with the problem of distortion in an initially well aligned bulk material placed in a field perpendicular to n and find that inertia effects can also lead to a roll structure in the problem.

Local probe in a Rayleigh-Benard experiment in liquid helium

Local probe in a Rayleigh-Benard experiment in liquid helium