Structure of hard-turbulent convection in two dimensions: Numerical evidence

Two-dimensional numerical simulations of a Boussinesq fluid demonstrate the dominant role played by the large-scale circulation in hard-turbulent Rayleigh-Bénard convection. The ‘‘roll’’ coordinates the motions of thermal plumes as they shuttle heat flux directly between the top and bottom boundaries. The roll also subjects the thermal boundary layers to a strong stabilizing shear exhibiting a simple power-law dependence on the Rayleigh number; this power law (∂u/∂z∝${\mathrm{Ra}}^{6/7}$) is predicted by a theory [Shraiman and Siggia, Phys. Rev. A 42, 3650 (1990)] which proposes the heat-transport (Nusselt-number) scaling relationship (Nu∝${\mathrm{Ra}}^{2/7}$) is determined solely by the structure of the thermal and viscous boundary layers. Also, the transition into two-dimensional hard turbulence is observed to coincide with the development of plumes which live sufficiently long to carry heat flux in the ‘‘wrong’’ direction. In addition to these issues of heat transport, the structure of the large-scale roll is investigated and the relationship between the turnover time ${\mathrm{\tau }}_0$ and the coherence frequency ${\mathrm{\omega }}_{\mathit{p}}$ is made precise.