Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestley's prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.     

On scaling laws in turbulent magnetohydrodynamic Rayleigh-Benard convection

We invoke the concepts of magnetic boundary layer and magnetic Rayleigh number and use the rates of magnetic energy dissipation in the bulk and the boundary layers to derive some scaling laws expressing how the Nusselt number depends on the magnetic Rayleigh number, Prandtl number and magnetic Prandtl number for the simple case of turbulent magnetohydrodynamic Rayleigh-Benard convection in the presence of a uniform vertical magnetic field.     

A HOLOGRAPHIC INTERFEROMETRY STUDY OF THE DOUBLE-DIFFUSIVE LAYERED SYSTEM

This study investigates double-diffusive convection in a two-layer, salt-stratified solution destablized by lateral Keating and cooling. The two-wavelength holographic interferometry method was used to measure the transient temperature, concentration, and density distributions. The evolution of the two-layered system can be divided into three stages. In the first stage, the thermally driven convective layers form rapidly, and the existing diffusion layer adjusts itself into a thin interface by convection motion. In the second stage, a quasi-steady state is attained. The temperature distribution is S-type and the temperature difference across the diffusion region does not change much. The concentration distribution is uniform in the two fluid layers, but the concentration and density differences decrease linearly with time. When the interface becomes very thin, unstable finger-type convection appears. Finally, the interface is destroyed by the boundary layers at the side walls in the third stage. The interfacial Nusselt number and Sherwood number art found to increase with the thermal Rayleigh number, and the effect of the solutal Rayleigh number seems to be less significant. The dimemumless mixing time is found to correlate well with thermal and solutal Rayleigh numbers. Results from numerical simulation are demonstrated and compared with the experiments.     

Mean velocity profile in confined turbulent convection

In this Letter, highly resolved measurements of the horizontal velocity inside the boundary layer of turbulent Rayleigh-Bénard convection are reported. They were performed in a cylindrical box with an aspect ratio Gamma=1.13 which was filled with air with a Prandtl number Pr=0.7. The horizontal velocity was measured along the central axis close to the cooling plate in a range of Rayleigh numbers between Ra=10;{11} and Ra=10;{12} using a two-dimensional laser Doppler velocimeter. We demonstrate that the profile of the mean velocity strongly differs from that of classical shear flows like the Blasius shape of a laminar flat plate boundary layer or a turbulent logarithmic velocity profile with standard coefficients.     

Fluctuating Thermal Boundary Layers and Heat Transfer in Turbulent Rayleigh–Bénard Convection

We investigate the effect of fluctuations in thermal boundary layer on heat transfer in turbulent Rayleigh–Bénard convection for Prandtl number greater than one in the regime where the thermal dissipation rate is dominated by boundary layer contribution and in the presence of a large-scale circulating flow.     

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in′a square cavity by direct numerical simulations.The Rayleigh number range is 1×10⁸≤Ra≤1×10¹³,and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max～(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10⁹,the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10¹⁰,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV～Ra?0.14±0.01.     

Combined action of different mechanisms of convective instability in multilayer systems

The nonlinear regimes of convection in a system of three immiscible viscous fluids are investigated by the finite-difference method. We study new phenomena caused by direct and indirect interaction of thermocapillary and buoyancy (Rayleigh and anticonvective) instability mechanisms. Two variants of heating-from below and from above-are considered. The interfaces are assumed to be flat. We focus on nonlinear evolution of steady and oscillatory motions and selection of stable convective structures depending on the parameters of systems. The influence of the lateral boundary conditions is also investigated. A classification of different variants of interaction between Rayleigh and thermocapillary instability mechanisms is presented, and several typical examples are studied. Specifically, we considered six different configurations where the Rayleigh convection arises mainly in a definite layer, and the thermocapillary convection appears mainly near the definite interface. Also, the case where both interfaces are active and alternatively play a dominant role is investigated. Some configurations of interaction between anticonvective and thermocapillary instability mechanisms are considered.     

Wave number selection in Rayleigh-Bénard convection: A numerical study

A phenomenological amplitude equation introduced earlier to calculate steady states of convection in a finite container, is studied numerically as a function of space and time. The effect of sidewalls on wave number selection is demonstrated by observing the response of the system to the sudden imposition of boundary conditions. The wave vectors of stable steady states are studied as a function of Rayleigh number near threshold, and it is shown that more than one state can be stable for fixed Rayleigh number.     

Coupling between aging and convective motion in a colloidal glass of Laponite

We study thermal convection in a colloidal glass of Laponite in formation. Low concentration preparation are submitted to destabilizing vertical temperature gradient, and present a gradual transition from a turbulent convective state to a steady conductive state as their viscosity increases. The time spent under convection is found to depend strongly on sample concentration, decreasing exponentially with mass fraction of colloidal particles. Moreover, at fixed concentration, it also depends slightly on the pattern selected by the Rayleigh Bénard instability: more rolls maintain the convection state longer. This behavior can be interpreted with recent theoretical approaches of soft glassy material rheology.     

Plumes and waves in two-dimensional turbulent thermal convection

We have conducted a high-resolution, two-dimensional direct numerical simulation of Rayleigh-Bénard convection with stress-free and periodic boundary conditions at a Rayleigh (Ra) number of 10(8) and Prandtl (Pr) number of unity. An aspect-ratio three box has been considered. A single cell has been used as the initial condition. First, the flow develops into time-dependent convection with a strong asymmetry and highly convoluted thermal plumes delineating a large-scale circulation. Smaller thermal plumes detach from the boundary layer and extend over the entire cell, creating a local inversion of the temperature gradient adjacent to the boundary layers. Then the conditions leading to the formation of internal waves are fulfilled, as the local Richardson number decreases sufficiently small to cross the linear threshold of Ri=0.25. Together with the strong shear, convective rolls with a Kelvin-Helmholtz wavelike character are produced. The secondary boundary layer itself becomes unstable and produces smaller plumes. At later times, the large-scale circulation is destroyed and the internal waves disappear. A Reynolds number, based on the global scale, of Re=500, is attained at this stage. Only isolated thermal plumes and vortices are present. Thus, internal waves can be generated at finite Prandtl number fluids for sufficiently high Ra in the presence of a large-scale circulation. Spectral analysis reveals that the kinetic energy decays with a logarithmic slope of -3, while the logarithmic slope of the thermal variance has a value of around -5 / 3.     

Onset of coherent oscillations in turbulent Rayleigh-Bénard convection

We report temperature cross correlation and velocity profile measurements in the aspect-ratio-one convection cell filled with water. A sharp transition from a random chaotic state to a correlated turbulent state of finite coherence time is found when the Rayleigh number becomes larger than a critical value Ra(c) approximately equal to 5 x 10(7). The experiment reveals a unique mechanism for the onset of coherent oscillations in turbulent Rayleigh-Bénard convection.     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

Stability of impulsively-driven natural convection with unsteady base state: implications of an adiabatic boundary

Stability conditions of a quiescent, horizontally infinite fluid layer with adiabatic bottom subject to sudden cooling from above are studied. Here, at difference from Rayleigh-Bénard convection, the temperature base state is never steady. Instability limits are studied using linear analysis while stability is analyzed using the energy method. Critical stability curves in terms of Rayleigh numbers and convection onset times were obtained for several kinematic boundary conditions. Stability curves resulting from energy and linear approaches exhibit the same temporal growth rate for large values of time, suggesting a bound for the temporal asymptotic behavior of the energy method.     

Boundary layer and scaling properties in turbulent thermal convection

Summary We describe an experiment which has been designed to measure both spatial and temporal features of turbulent thermal convection in a fluid layer heated from below. Specifically we have studied the dependence of the heat flowvs. the Rayleigh number, the thermal boundary layer profile, the temperature probability distribution function, the frequency and wave number power spectra. All the results have been compared with recent theories. The relevant scales of the problem, the Bolgiano and dissipative lengths, are also computed as a function of control parameters.     

Dependence of heat transport on the strength and shear rate of prescribed circulating flows

We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), which measures the heat transport, scales with the normalized shear rate to an exponent 1/3. On the other hand, when the side-boundary thermal layer is thicker, the dependence of Nu on the Peclet number, which measures the maximum velocity, or the normalized shear rate when the viscous boundary layer thickness is fixed, is generally not a power law. Scaling behavior is obtained only in an asymptotic regime. The relevance of our results to the problem of heat transport in turbulent convection is also discussed. Received 28 November 2001 Published online 25 June 2002     

Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection

We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from 2x10(7) to 3x10(10), all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about 20% over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.     

Transient reemergent order in convective spatial chaos

Transient turbulent states leading to a stable convective structure have been observed in Rayleigh-Bénard convection at high Rayleigh number and in confined geometry. This turbulent state consists in alternating sequences of spatial chaos stochastically interrupted by intermittent lockings on definite convective structures.     

Variational bounds on shear-driven turbulence and turbulent Boussinesq convection

Based on earlier studies by Hopf (1941), Doering and Constantin (1992, 1994, 1995) have recently formulated a new “background” technique for obtaining upper bounds on turbulent fluid flow quantities. This method produces upper bounds on the limit supremum of long time averages, making no statistical assumptions about the flow in contrast to the well-known Howard-Busse approach. The full optimisation problems posed by this method for the momentum transport in turbulent Couette flow and the heat transport (with zero background flow) in turbulent Boussinesq convection are solved here for the first time at asymptotically large Reynolds number and Rayleigh number within Busse's multiple boundary layer approximation to extract the best (lowest) possible upper bounds available. Intriguingly, the original bounds isolated by Busse (1969, 1970) within the confines of statistical stationarity are recovered exactly using this new formalism. The optimal background velocity profile for turbulent Couette flow is found to be shearless in the interior thus differing from Busse's “ ” mean shear result. In the convective case, an interesting degeneracy in the formulation of the background variational problem leads to an indeterminacy in the optimal background temperature profile. Only for one special choice is the isothermal core feature of Busse's mean profile recovered.