TY - JOUR

T1 - Transition to turbulent thermal convection beyond [Formula Presented] detected in numerical simulations

AU - Vincent, Alain P.

AU - Yuen, David A.

PY - 2000/1/1

Y1 - 2000/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0001725338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001725338&partnerID=8YFLogxK

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 -