Phase transition to intermittent velocity gradient statistics in thermal convection

热对流中的相变到间歇速度梯度统计

• 批准号: 417275129
• 负责人: Professor Dr. Jörg Schumacher
• 金额: --
• 依托单位: Department of Mechanical Engineering
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/417275129?language=en
• 关键词: Phase; transition; intermittent; velocity; gradient; Phase; transition; intermittent; velocity; gradient

The question of small-scale universality is one of the fundamental problems in turbulence research. It is a main ingredient of all turbulence models which rely on the assumption that there is a generic cascade of kinetic energy from large to small scales at which velocity fluctuations then are dissipated following the same statistical laws. Rather than studying therefore the statistics in the fully developed cascade range at high Reynolds numbers, the interest has turned in the past years to analyses of the Reynolds number dependence of statistical moments of velocity derivatives which are mainly supported at small scales. Recently, a phase transition to an intermittent, non-Gaussian velocity gradient statistics for Reynolds numbers as small as 100 has been predicted and found for an isotropic box flow which is driven randomly. The purpose of the present proposal is to investigate if such a phase transition to non-Gaussian statistical behavior of velocity derivatives can be generalized to turbulent flows in the presence of walls and how the statistical moments in the transition range are affected by the present boundary layer dynamics. The flow that will be studied here, is a Rayleigh-Bénard convection flow where thermal plumes detach from the walls and drive statistical fluctuations of velocity and velocity derivatives in the bulk of the layer.

小规模普遍性的问题是湍流研究中的基本问题之一。它是所有湍流模型的主要诱导模型，依赖于以下假设：从大到小尺度上有一系列通用的动能级联，然后遵循相同的统计定律消散速度波动。有趣的不是在高雷诺数上以全面开发的级联范围内的统计数据进行统计数据，而是在过去几年中转变为分析雷诺数数量的依赖性，这对速度衍生物的统计矩依赖性依赖性，这些速度衍生物的统计矩依赖于小规模。最近，已经预测并发现了与随机驱动的各向同性盒流量的间歇性非高斯速度梯度统计的相变为100至100。本提案的目的是研究速度衍生物的非高斯统计行为是否可以推广到存在壁的存在以及过渡范围内的统计矩如何受到当前边界层动力学的影响。这里将研究的流量是雷利 - 纳德会议流，其中热羽可以从墙壁上分离，并驱动层中速度和速度衍生物的统计波动。