Enard System Research Articles

Phase diagram of externally modulated Rayleigh-Bénard system near the codimension-two point.

The phase diagram of an externally modulated Rayleigh-B\'enard system of binary mixtures near the codimension-two (CT) point is analyzed. The amplitude equation associated with this system is considered and the dynamical behavior is obtained by numerical integration of the equations of motion. We find that close to the CT point the system exhibits chaotic behavior, which in some region of the phase diagram coexists with the conductive state. It is suggested that these features may be observed experimentally even for small amplitude of the modulation as compared with the critical temperature difference \ensuremath{\Delta}${T}_{c}$ of the unmodulated system.

Global universality at the onset of chaos: Results of a forced Rayleigh-Benard experiment.

We study an experimental orbit on a two-torus with a golden-mean winding number obtained from a forced Rayleigh-B\'enard system at the onset of chaos. This experimental orbit is compared with the orbit generated by a simple theoretical model, the circle map, at its golden-mean winding number at the onset of chaos. The of singularities of the two orbits are compared. Within error, these are identical. Since the spectrum characterizes the metric properties of the entire orbit, this result confirms theoretical speculations that these orbits, taken as a whole, enjoy a kind of universality.

Thermal convection under external modulation of the driving force. II. Experiments.

Experimental data are presented on the temperature response of a Rayleigh-B\'enard system to sinusoidal modulation of the heat current supplied to the lower plate near the onset of convection. Quantitative results are obtained for the average convective current as a function of the average Rayleigh number and of the amplitude and frequency of the modulation. Results are also presented on the temporal behavior of the response, above the convective threshold. The data are interpreted in terms of a previously proposed model which is a generalization of the Lorenz equations to periodic external driving. An important effect included in the model is the dynamic thermal mismatch between the sidewalls and the fluid which leads to an imperfect bifurcation between the conductive and convective states. As a result, the upward shift of the convective threshold caused by modulation in the ideal system is masked by the presence of sidewalls. In our model, this effect is controlled by a single adjustable parameter which turns out to agree in order of magnitude with previous experimental and theoretical estimates pertaining to a lower frequency range. The detailed comparison between experiment and theory shows good qualitative agreement, and some quantitative discrepancies in the parameter range explored. Suggestions are made for additional experiments to test a larger parameter range and in particular to minimize the sidewall effect in order to approximate the ideal threshold behavior more closely.

Stability analysis of two-dimensional models of three-dimensional convection.

Analytical and numerical methods are used to study the linear stability of spatially periodic solutions for various two-dimensional equations which model thermal convection in fluids. This analysis suggests new model equations that will be useful for investigating questions such as wave-number selection, pattern formation, and the onset of turbulence in large-aspect-ratio Rayleigh-B\'enard systems. In particular, we construct a nonrelaxational model that has stability boundaries similar to those calculated for intermediate Prandtl-number fluids.

External Noise and the Onset of Turbulent Convection

The effect of fluctuations on the transition to turbulence is examined by introducing large-amplitude noise into the boundary temperature of a Rayleigh-B\'enard system. The response can be largely described in terms of variables whose induced fluctuations are much slower than either the natural oscillations or the external noise. However, the sequence of transitional regimes and the statistical properties of the turbulent state are not dramatically affected.

Turbulence near Onset of Convection

New long-term (days) measurements of the evolution of turbulence for a Rayleigh-B\'enard system with aspect ratio $\ensuremath{\Gamma}=4.72$ reveal a turbulent state, with a threshold near the critical Rayleigh number ${R}_{c}$, which consists of a random background time dependence and rare, randomly spaced, major events. These events are discussed in terms of the analog of a particle under the influence of a stochastic driving force and in a potential with two minima.