Self-organized criticality of turbulence in strongly stratified mixing layers
Self-organized criticality of turbulence in strongly stratified mixing layers
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强分层混合层中湍流的自组织临界性
DOI：
10.1017/jfm.2018.695
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发表时间：
2018
影响因子：
3.7
通讯作者：
Colm‐cille P. Caulfield
中科院分区：
文献类型：
--
作者：
H. Salehipour;W. Peltier;Colm‐cille P. Caulfield
由于分层剪切流在地球物理和环境条件下的重要性，我们通过对各种初始条件下 Holmboe 波不稳定性 (HWI) 产生的湍流进行一系列直接数值模拟来表征其能量、混合和光谱行为。我们关注的是分层足够“强”的情况，因此 HWI 是流动的主要不稳定性。我们的数值研究结果表明，自组织临界性（SOC）的出现，表现为对与水平平均平均流相关的适当定义的梯度理查森数 $Ri_{g}$ 进行调整，使其不断被吸引向 $Ri_{g}\sim 1/4$ 临界值。这种自组织通过不断强化的“冲刷”运动（即“雪崩”）局部化而发生，这些运动是 Holmboe 波不稳定性破坏引起的湍流的特征，并在尖锐局部密度界面的上侧和下侧发展，嵌入在更分散的剪切层内。还发现这些局部“雪崩”表现出预期的尺度不变特征。从能量学的角度来看，SOC 的出现表现为长期存在的湍流的形式，该湍流在较长时间内保持“准平衡”状态。最重要的是，这种自组织行为产生的不可逆混合似乎一般以通用累积湍流通量系数 $\unicode[STIX]{x1D6E4}_{c}\sim 0.2$ 为特征，仅适用于 Holmboe 波不稳定性产生的湍流。这种自组织临界状态的存在证实了与分层湍流的自我调节相关的原始物理论点，即涉及特纳所描述的“一种平衡”（1973，流体中的浮力效应，剑桥大学出版社）。
Motivated by the importance of stratified shear flows in geophysical and environmental circumstances, we characterize their energetics, mixing and spectral behaviour through a series of direct numerical simulations of turbulence generated by Holmboe wave instability (HWI) under various initial conditions. We focus on circumstances where the stratification is sufficiently ‘strong’ so that HWI is the dominant primary instability of the flow. Our numerical findings demonstrate the emergence of self-organized criticality (SOC) that is manifest as an adjustment of an appropriately defined gradient Richardson number, $Ri_{g}$ , associated with the horizontally averaged mean flow, in such a way that it is continuously attracted towards a critical value of $Ri_{g}\sim 1/4$ . This self-organization occurs through a continuously reinforced localization of the ‘scouring’ motions (i.e. ‘avalanches’) that are characteristic of the turbulence induced by the breakdown of Holmboe wave instabilities and are developed on the upper and lower flanks of the sharply localized density interface, embedded within a much more diffuse shear layer. These localized ‘avalanches’ are also found to exhibit the expected scale-invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a ‘quasi-equilibrium’ state for an extended period of time. Most importantly, the irreversible mixing that results from such self-organized behaviour appears to be characterized generically by a universal cumulative turbulent flux coefficient of $\unicode[STIX]{x1D6E4}_{c}\sim 0.2$ only for turbulent flows engendered by Holmboe wave instability. The existence of this self-organized critical state corroborates the original physical arguments associated with self-regulation of stratified turbulent flows as involving a ‘kind of equilibrium’ as described by Turner (1973, Buoyancy Effects in Fluids, Cambridge University Press).