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
σ=0.5
. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter
ϵ
. 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.