Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

Abstract

We present the first large scale numerical simulation of three-dimensional Rayleigh-Bénard convection near onset, under free-free boundary conditions for a fluid of Prandtl number $\sigma =0.5$. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter $\epsilon$. We conclude that the transition from conduction to spatiotemporal chaos is second order and of ``mean field'' character. We also present a simple theory for the time-averaged convective current. Finally, we show that the time-averaged structure factor satisfies a scaling behavior with respect to the correlation length near onset.

5 pages, 5 figures, to appear in Phys. Rev. Lett

References in corpus (2)

• Spiral defect chaos in a model of Rayleigh-Benard convection
• Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy

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• Homoclinic bifurcations in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation
• Zero-Prandtl-number convection with slow rotation
• The Domain Chaos Puzzle and the Calculation of the Structure Factor and Its Half-Width
• Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box