Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

Details Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

1996-10-07

arxiv.org/abs/patt-sol/9610005v2

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevLett.78.1046

We present the first large scale numerical simulation of three-dimensional Rayleigh-B\'enard 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.

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