Phase transition to intermittent velocity gradient statistics in thermal convection

小尺度普遍性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组成部分，这些模型依赖于这样的假设，即从大尺度到小尺度存在动能的一般级联，然后速度波动按照相同的统计规律消散。因此，在过去几年中，人们的兴趣已转向分析主要在小尺度上支持的速度导数的统计矩的雷诺数依赖性，而不是研究在高雷诺数下充分发展的叶栅范围内的统计数据。最近，一个间歇性的相变，非高斯的速度梯度统计雷诺数小至100已被预测和发现的各向同性盒流是随机驱动的。本建议的目的是调查，如果这样的相变到非高斯统计行为的速度导数可以推广到湍流中存在的墙壁和如何在过渡范围内的统计矩是由目前的边界层动力学的影响。这里将要研究的流动是瑞利-贝纳德对流，其中热羽流从壁分离，并驱动层中大部分速度和速度导数的统计波动。

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.