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

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中的湍流，都是由对流驱动的，并且受到快速旋转的强烈约束，一个优秀且易于数学描述的模型系统是旋转瑞利-贝纳德对流模型。由限制在围绕垂直轴旋转的热底部边界和冷顶部边界之间的液体或气体组成，但湍流水平和相对旋转速率（以控制参数表示）。在瑞利-贝纳德对流的地球数值模拟和实验室实验中达到的瑞利和埃克曼数，并不像自然环境中的参数那么极端。此外，大多数数值模拟和数学理论都假设材料属性（例如粘度和热）恒定。扩散率），与现实流体相反，现实流体随温度和压力变化。因此，根据地球物理和天体物理流解释模拟和实验的结果有些问题。但是，存在一个问题。湍流研究中长期坚持的原则是，如果流动变得足够湍流，即达到“最终状态”，任何全局传输和宏观特征都变得独立于分子扩散率，特别是粘度和热扩散率。至关重要的是，如果最终状态存在，尽管控制参数存在许多数量级的差异，但从数值模拟和实验室实验到地球和天体物理系统的升级是可能的。拟议研究的目的是测试。在快速旋转的瑞利-贝纳德对流的最终状态下，热量和动量传输的无扩散缩放的假设。尽管理论论证预测旋转系统比非旋转系统更容易达到最终状态，但数值分辨率要求对于当今计算资源的强力方法来说是令人望而却步的。为了减轻分辨率限制，我将通过在同一对流容器内采用不同的热扩散率和运动粘度来考虑一种新颖的观点。材料属性的变化会导致经典（非终极）瑞利-贝纳德问题中上下对称性的破坏，但是，在最终状态下，假设分子扩散率确实如此，人们可能会期望这种对称性得到恢复。不再影响全局流动状态。这种对称性的恢复可以用作达到最终状态的指标和衡量标准，并且可以定量地进行可靠的推断。此外，众所周知，边界层是热量传输和传输的关键因素。势头在对于湍流热对流，我将比较边界层自由三周期瑞利-贝纳德对流的模拟与包含边界层的类似实验室的圆柱形装置。

项目成果

Transition from wall modes to multimodality in liquid gallium magnetoconvection

• DOI: 10.1103/physrevfluids.8.103503
• 发表时间: 2023-10
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Yufan Xu;S. Horn;J. Aurnou

Thermoelectric precession in turbulent magnetoconvection

湍流磁对流中的热电进动

• DOI: 10.1017/jfm.2021.880
• 发表时间: 2022
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Xu, Yufan;Horn, Susanne;Aurnou, Jonathan M.
• 通讯作者: Aurnou, Jonathan M.

Unravelling the large-scale circulation modes in turbulent Rayleigh-Bénard convection (a)

揭示湍流瑞利-贝纳德对流中的大尺度环流模式 (a)

• DOI: 10.1209/0295-5075/ac3da2
• 发表时间: 2021
• 期刊: Europhysics Letters
• 作者: Horn, Susanne;Schmid, Peter J.;Aurnou, Jonathan M.
• 通讯作者: Aurnou, Jonathan M.