TY - JOUR
T1 - Transition to turbulent thermal convection beyond [Formula Presented] detected in numerical simulations
AU - Vincent, Alain P.
AU - Yuen, David A.
PY - 2000
Y1 - 2000
N2 - We have conducted high-resolution two-dimensional calculations for a Boussinesq convection model with a Prandtl number of unity in an aspect-ratio 3 box, going from Rayleigh numbers between [Formula Presented] to [Formula Presented] A grid of [Formula Presented] grid points consisting of a cosine-sine basis set has been employed for free-slip boundary conditions. We have found evidence for a transition involving the branching of plumes at a Rayleigh number of [Formula Presented] Inside the core of these “superplumes,” the structure is extremely complex. There may be another transition at Ra of [Formula Presented] where a secondary instability may develop in regions of the local Rayleigh number which becomes supercritical inside the core of the complex “superplumes.” For Ra of [Formula Presented] to [Formula Presented] Ra follows a [Formula Presented] power law in the Nusselt-Rayleigh number relationship. From Ra of [Formula Presented] to [Formula Presented] Ra follows a [Formula Presented] power law. Above this value the Nusselt number becomes insensitive to the variation in the global Rayleigh number and this is due to the development of small-scale convection cells vertically aligned in the interior of the extremely high Ra number flow. The global Reynolds number scales as [Formula Presented] up to Ra of [Formula Presented] Scaling relationships based on global properties would not work in extremely high Ra situations beyond Ra of [Formula Presented] because of the complex turbulent layered convection in the core of the flow and the severe degradation of the boundary layers.
AB - We have conducted high-resolution two-dimensional calculations for a Boussinesq convection model with a Prandtl number of unity in an aspect-ratio 3 box, going from Rayleigh numbers between [Formula Presented] to [Formula Presented] A grid of [Formula Presented] grid points consisting of a cosine-sine basis set has been employed for free-slip boundary conditions. We have found evidence for a transition involving the branching of plumes at a Rayleigh number of [Formula Presented] Inside the core of these “superplumes,” the structure is extremely complex. There may be another transition at Ra of [Formula Presented] where a secondary instability may develop in regions of the local Rayleigh number which becomes supercritical inside the core of the complex “superplumes.” For Ra of [Formula Presented] to [Formula Presented] Ra follows a [Formula Presented] power law in the Nusselt-Rayleigh number relationship. From Ra of [Formula Presented] to [Formula Presented] Ra follows a [Formula Presented] power law. Above this value the Nusselt number becomes insensitive to the variation in the global Rayleigh number and this is due to the development of small-scale convection cells vertically aligned in the interior of the extremely high Ra number flow. The global Reynolds number scales as [Formula Presented] up to Ra of [Formula Presented] Scaling relationships based on global properties would not work in extremely high Ra situations beyond Ra of [Formula Presented] because of the complex turbulent layered convection in the core of the flow and the severe degradation of the boundary layers.
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U2 - 10.1103/PhysRevE.61.5241
DO - 10.1103/PhysRevE.61.5241
M3 - Article
AN - SCOPUS:0001725338
SN - 1063-651X
VL - 61
SP - 5241
EP - 5246
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 5
ER -