Phase transition to intermittent velocity gradient statistics in thermal convection

小尺度普适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，这些模型依赖于这样一个假设，即存在一个从大尺度到小尺度的一般的动能级联，在这个级联中，速度波动遵循相同的统计规律消散。因此，在过去的几年里，人们的兴趣不再是研究高雷诺数下完全发展的叶栅范围内的统计，而是转向了分析速度导数的统计矩对雷诺数的依赖，这主要是在小尺度上得到支持的。最近，对于随机驱动的各向同性箱形流，预测并发现了一个向间歇性非高斯速度梯度统计的相变，雷诺数小至100。本文的目的是研究这种速度导数的非高斯统计行为的相变是否可以推广到有壁面的湍流中，以及在过渡范围内的统计矩如何受到当前边界层动力学的影响。这里要研究的流动是瑞利-巴姆纳德对流，其中热羽流从壁上分离，并在大部分层中驱动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.