Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

We present a large scale numerical simulation of three-dimensional Rayleigh-B\'enard convection near onset, under free-free boundary conditions for a fluid of Prandtl number σ0ex0ex=0ex0ex0.5. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter. 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.