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首页> 外文期刊>Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics >Transition to turbulent thermal convection beyond Ra=10(10) detected in numerical simulations
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Transition to turbulent thermal convection beyond Ra=10(10) detected in numerical simulations

机译：在数值模拟中检测到超过Ra = 10（10）的湍流热对流过渡

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摘要

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 10(8) to 10(14). A grid of 1024 X 3076 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 10(10). Inside the core of these "superplumes," the structure is extremely complex. There may be another transition at Ra of 10(12) 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 10(8) to 10(10), Ra follows a 1/3 power law in the Nusselt-Rayleigh number relationship. From Ra of 10(10) to 10(12), Ra follows a 1/2 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 Re approximate to Ra-1/4 up to Ra of 10(14). Scaling relationships based on global properties would not work in extremely high Ra situations beyond Ra of 10(12) because of the complex turbulent layered convection in the core of the flow and the severe degradation of the boundary layers. [References: 36]
机译：我们对宽高比为3的框内具有Prandtl数的Boussinesq对流模型进行了高分辨率的二维计算，其瑞利数在10（8）到10（14）之间。自由滑移边界条件已采用由余弦-正弦基集组成的1024 X 3076网格点的网格。我们已经找到了涉及瑞利数为10（10）的羽状分支的过渡的证据。在这些“超级柱”的核心内部，结构极为复杂。在Ra的10（12）处可能会有另一个过渡，在该处可能会在局部Rayleigh区域中形成次级不稳定性;该数目在复杂的“超级羽”的核心内部变得超临界。对于10（8）至10（10）的Ra，在Nusselt-Rayleigh数关系中，Ra遵循1/3幂定律。从10（10）的Ra到10（12），Ra遵循1/2幂定律。高于该值时，Nusselt数对全局瑞利数的变化变得不敏感，这是由于在极高的Ra数流内部垂直排列的小型对流单元的发展所致。雷诺数的整体范围由Re近似为Ra-1 / 4到Ra（10（14））。由于流动核心中复杂的湍流分层对流以及边界层的严重退化，基于全局属性的比例关系在Ra超出10（12）的极高Ra情况下将不起作用。 [参考：36]

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