Non-Oberbeck-Boussinesq Effects in the Ultimate State of Rapidly Rotating Rayleigh-Benard Convection

快速旋转瑞利-贝纳德对流终极状态下的非奥伯贝克-布辛涅斯克效应

• 批准号: EP/V047388/1
• 负责人: Susanne Horn
• 金额: $ 30.05万
• 依托单位: Coventry University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV047388%2F1
• 关键词: Non; Oberbeck; Boussinesq; Effects; Ultimate; Non; Oberbeck; Boussinesq; Effects; Ultimate

Many of the turbulent flows occurring in nature, for example within planetary and stellar interiors, as well as atmospheres, are driven by convection and are strongly constrained by rapid rotation. An excellent and mathematically easily describable model system is rotating Rayleigh-Bénard convection. The model consists of a liquid or gas confined between a warm bottom boundary and a cold top boundary rotated around the vertical axis. But the level of turbulence and the relative rotation rates (expressed in terms of the control parameters Rayleigh and Ekman number) reached in earthbound numerical simulations and laboratory experiments of Rayleigh-Bénard convection, are not as extreme (yet) as the parameters in natural settings. Moreover, most numerical simulations and mathematical theories assume constant material properties (e.g. viscosity and thermal diffusivity), contrary to realistic fluids where they vary with temperature and pressure. Thus, interpreting results from simulations and experiments in the light of geophysical and astrophysical flows is somewhat problematic.However, there is a long-held tenet in turbulence research that if the flow only becomes turbulent enough, that is, reaches the "ultimate regime," any global transport and macroscopic features become independent of the molecular diffusivities, in particular, the viscosity and the thermal diffusivity. Hence, crucially, if the ultimate state exists, an upscaling from numerical simulations and laboratory experiments to geo- and astrophysical systems is possible despite many orders of magnitude difference in the control parameters. The objective of the proposed research is to test the hypothesis of a diffusion-free scaling of the heat and momentum transport in the ultimate state of rapidly rotating Rayleigh-Bénard convection.Even though theoretical arguments predict that the ultimate state is more easily accessible in rotating than in non-rotating systems, the numerical resolution requirements are prohibitive for a brute force approach with present-day computational resources.To alleviate the resolution constraints, I will consider a novel point of view by employing a varying thermal diffusivity and kinematic viscosity within the very same convection vessel. The variation of the material properties leads to a breaking of the top-bottom symmetry in the classical (non-ultimate) Rayleigh-Bénard problem. However, in the ultimate regime, one may expect that this symmetry gets restored, assuming that the molecular diffusivities do no longer affect the global flow state. The restoration of this symmetry can be used as an indicator and quantitative measure for reaching the ultimate regime and allows for reliable extrapolation. Further, as boundary layers are known to be key players in the transport of heat and momentum in turbulent thermal convection, I will compare simulations of boundary layer free triply periodic Rayleigh-Bénard convection with laboratory-like cylindrical set-ups that include boundary layers.

自然界中发生的许多湍流，例如行星和恒星内部以及大气都受到连接的驱动，并受到快速旋转的强烈限制。出色且数学上易于描述的模型系统是旋转Rayleigh-Bénard的结构。该模型由限制在温暖的底部边界之间的液体或气体组成，围绕垂直轴旋转的冷顶边界。但是，在雷利 - 纳德构造的地球数值模拟和实验室实验中达到的湍流和相对旋转速率（根据控制参数和埃克曼编号表示）并不像自然设置中的参数那样极端（尚未）。此外，大多数数值模拟和数学理论都具有恒定的材料特性（例如粘度和热难度），与它们随温度和压力变化而变化的逼真的流体对比。根据地球物理和天体物理流的模拟和实验，解释是有些问题的。但是，在湍流研究中存在一个长期以来的宗旨，即如果流量仅变得足够湍流，即达到“最终状态”，任何全球运输和宏观特征都会独立于分子扩散率，尤其是粘度和热扩散性。因此，完全，如果存在最终状态，则可以从数值模拟和实验室实验到地理和天体物理系统的升级，尽管控制参数的数量级差异很大。拟议的研究的目的是测试在迅速旋转的雷利 - 贝纳德结构的最终状态下，热量和动量传输的无扩散缩放的假设。尽管理论上的论点在旋转方面更容易易于旋转，而不是在非互化系统中更容易访问，而不是在不互动的系统中进行统一的分辨率，而对于目前的资源，则可以在数字上进行限制。通过在同一施工容器中采用不同的热难度和运动式粘度，一种新颖的观点。材料特性的变化导致在经典（非文化）雷利 - 贝纳德问题中破坏顶底对称性。但是，在最终的状态下，假设分子差异不再影响全球流状态，人们可能会期望这种对称性会恢复。该对称性的恢复可以用作达到最终状态的指标和定量措施，并允许可靠的外推。此外，由于众所周知，边界层是湍流热转化中热量和动量运输中的关键参与者，因此我将比较边界层的模拟免费三重周期性周期性的雷利 - 纳德连接与实验室样圆柱形设置（包括边界层）。