Nard Convection Research Articles

Large-scale turbulence in Rayleigh-B�nard convection

Rayleigh-Benard convection in a plane layer with poorly conducting boundaries is considered. Two-dimensional equations, asymptotically exact for small supercriticalities, are obtained for describing largescale flows whose characteristic dimensions considerably exceed the thickness of the layer. An increase in the dimensions of the layer in plan and higher levels of supercriticality lead to complex turbulent motions of the fluid which are investigated by network methods and by means of an hierarchical model of turbulence. It is shown that the kinetic energy accumulates in the largest eddies, and that the temperature fluctuation spectrum has a maximum at intermediate scales.

Noise-induced intermittency in the quasiperiodic regime of Rayleigh-B�nard convection

Thermal measurements on a converting dilute3He-superfluid4He solution in the quasiperiodic regime show a transition from a mode-locked periodic state to chaotic time dependence via intermittency. The type of intermittency is discussed in the context of standard models of the phenomenon. In a region just below the onset of intermittency, injection of external multiplicative noise with noise amplitude above a certain threshold level induces the chaotic state. This noise-induced transition can be understood to be due to perturbations of a system with a barely stable attractor; the noise causes the system to escape the weakly attracting periodic points. We present a numerical simulation of a 1D map with external noise which explains some aspects of the noise-induced behavior, and a 2D map which has certain features of the intermittency.

Wavelength selection in Rayleigh-B�nard convection

Rayleigh-Benard convection is considered in the presence of a weakly nonuniform temperature distribution and weakly nonuniform layer height with their gradients perpendicular to the (parallel) convection rolls. In the infinite Prandtl number limit the phase equation that describes the slow spatial and temporal evolution of the local wave number is derived. Evaluating the equation near threshold and for stress-free boundary conditions we find nonuniversal wavenumber selection, forced phase diffusion with moving patterns, and other measurable effects.

On Rayleigh-B�nard convection with rotation and magnetic field

A sufficient condition for the validity of the principle of exchange of stabilities in the Rayleigh-Benard convection problem under the simultaneous action of a uniform vertical rotation and magnetic field is derived. Furthermore the complex growth rate of an arbitrary oscillatory perturbation, neutral or unstable, is shown to lie inside a semicircle in the right half of the complexp-plane. These results are uniformly valid for all combinations of free insulating, rigid perfectly conducting and rigid insulating boundaries.

Mean square velocities of b�nard convection and heat transfer

The approximate formula K ∩ a−2R(N−1), where a is a constant near 9 and R and N are the Rayleigh and Nusselt numbers, was proposed in [1] for the dimensionless kinetic energy K of convection in a horizontal layer of liquid. It is shown in the present paper that this expression is exact in linear and weakly nonlinear convection theory when the velocity and temperature fields are represented analytically [2–4]. The valuea is found to be 8.76 when the upper and lower boundaries of the layer are solid walls. The results are given of numerical calculations of the kinetic energy of the convection and the heat transfer in a wide range of Rayleigh numbers (up to 44 000) and Prandtl numbers (0.025 ⩽ P ⩽ 15). Analysis of the results shows that a is in fact a weak function of both R and P. If this is also the case at large R, it indicates a certain breaking of scaling of the mean convection characteristics at sufficiently large values of the Rayleigh number. It also indicates why laboratory experiments give values of n in the dependence N ∼ Rn which are generally slightly less than the theoretical value n = 1/3.