[论文解读] Diffusion of turbulence following both stable and unstable step stratification perturbations

Luca Gallana, Shahbozbek Abdunabiev+2 more|arXiv (Cornell University)|Jan 18, 2022

Particle Dynamics in Fluid Flows参考文献 42被引用 4

一句话总结

本研究利用6m×6m×12m域内的三维直接数值模拟（DNS），在泰勒微尺度雷诺数Re = 250的条件下，研究了在稳定与不稳定热层结下，非饱和水汽云界面处的湍流混合。结果表明，稳定层结抑制了混合，引发动能耗散并降低各向异性；而不稳定层结则增强了瞬时动能增长，提高混合强度，并放大纵向速度梯度的差异，其能量衰减遵循依赖于层结强度的代数标度律。

ABSTRACT

The evolution of a two-phase, air and unsaturated water vapor, time decaying, shearless, turbulent layer has been studied in the presence of both stable and unstable perturbations of the normal temperature lapse rate. The top interface between a warm vapor cloud and clear air in the absence of water droplets was considered as the reference dynamics. Direct, 3D numerical simulations were performed within a 6m x 6m wide and 12m high cloud portion, which was hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor micro-scale Reynolds' number was 250 inside the cloud portion. The squared Froude's number varied over intervals of [0.4; 1038.5] and [-4.2; -20.8]. A sufficiently intense stratification was observed to change the mixing dynamics. The formation of a sub-layer inside the shearless layer was observed. The sub-layer, under a stable thermal stratification condition, behaved like a pit of kinetic energy. On the other hand, it was observed that kinetic energy transient growth took place under unstable conditions, which led to the formation of an energy peak just below the center of the shearless layer. The scaling law of the energy time variation inside the interface region was quantified: this is an algebraic law with an exponent that depends on the perturbation stratification intensity. The presence of an unstable stratification increased the differences in statistical behavior among the longitudinal velocity derivatives, compared with the unstratified case. Since the mixing process is suppressed in stable cases, small-scale anisotropy is also supressed.

研究动机与目标

• 理解热层结（稳定与不稳定）如何影响暖水汽云与清晰空气界面处的湍流混合动力学。
• 研究层结在无剪切、随时间衰减的湍流层中对动能分布、耗散率及各向异性的影响。
• 量化在不同层结强度下，湍流能量衰减的标度行为。
• 考察层结对被动标量输运及速度脉动谱特性的影响。

提出的方法

• 对代表云-空气界面部分的6m×6m×12m大气域进行了三维直接数值模拟（DNS），模拟水汽云界面处的湍流混合。
• 在纳维-斯托克斯方程与能量方程中应用Boussinesq近似，以模拟不可压缩、热层结流动。
• 采用二维模板并行化方法，在无拉格朗日水滴追踪的条件下实现高空间分辨率与高效计算。
• 通过改变平方弗劳德数在稳定层结下为[0.4; 1038.5]，在不稳定层结下为[-4.2; -20.8]，以探究层结强度的影响。
• 追踪界面处的速度脉动、动能、耗散率及被动标量输运。
• 分析速度分量的谱行为及耗散率的概率密度函数，以评估各向异性和自相似性。

实验结果

研究问题

• RQ1 在无剪切、衰减的湍流层中，稳定热层结如何影响湍流动能与混合动力学的演化？
• RQ2 在不同层结强度下，界面区域湍流能量衰减的标度行为如何？
• RQ3 不稳定层结如何影响动能的瞬时增长及纵向速度梯度统计行为？
• RQ4 层结在多大程度上改变了速度脉动的谱特性，特别是垂直与水平分量？
• RQ5 层结如何影响耗散率及其概率密度函数的自相似性，特别是在混合层中？

主要发现

• 在稳定层结下，形成一个类似动能洼地的亚层，湍流扩散与夹带过程被强烈抑制。
• 在Fr² = 0.4时，观察到持续1.4–3.5个涡旋周转时间的出流阶段，表明低弗劳德数下混合被抑制。
• 在Fr² = 4.2时，稳定层结使耗散率增加70%；而在Fr² = -4.2时，不稳定层结使耗散率降低2%。
• 界面区域能量衰减时间的变化遵循代数标度律，其指数依赖于扰动层结的强度。
• 不稳定层结增强了纵向速度梯度统计行为的差异，增加了小尺度各向异性和流体丝压缩。
• 耗散率的概率密度函数呈对数正态分布且在各层中具有自相似性，表明层结对涡旋结构中能量的影响大于对其形态的影响。