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

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.

小尺度普遍性问题是湍流研究的基本问题之一，它是所有湍流模型的主要组成部分，这些模型都依赖于这样的假设：存在从大尺度到小尺度的一般动能级联，在该级联下速度波动。因此，在过去几年中，人们的兴趣已经转向分析速度导数统计矩的雷诺数依赖性，而不是研究高雷诺数下完全开发的级联范围内的统计数据。最近，对于小至 100 的雷诺数，已预测并发现了随机驱动的各向同性盒流的间歇性非高斯速度梯度统计的相变。本提案的目的是。研究速度导数的非高斯统计行为的这种相变是否可以推广到存在壁的湍流，以及过渡范围内的统计力矩如何受到当前边界层动力学的影响。这里要研究的是瑞利-贝纳德对流，其中热羽流从壁上分离并驱动层内大部分速度和速度导数的统计波动。