强分层混合层中turbulence的自组织临界性
Self-organized criticality of turbulence in strongly stratified mixing layers
摘要：
出于分层剪切流在地球物理和环境条件下的重要性，我们通过一系列直接数值模拟的湍流Holmboe波不稳定性（HWI）在各种初始条件下产生的能量，混合和光谱行为的特点。我们专注于分层的情况下，是足够的“强”，使HWI是占主导地位的流动的主要不稳定性。我们的数值研究结果表明，出现自组织临界性（SOC），这是表现为一个适当定义的梯度理查森数，$Ri_g$，与水平平均流量的调整，在这样一种方式，它是不断吸引到一个临界值$Ri_g \sim 1/4$。这种自组织是通过“冲刷”运动（即“雪崩”）的连续强化局部化而发生的，“冲刷”运动是由Holmboe波不稳定性的预锻引起的湍流的特征，并在急剧局部化的密度界面的上下两侧发展，嵌入在更加扩散的剪切层中。这些本地化的“雪崩”也被发现表现出预期的规模不变的特点。从能量学的角度来看，SOC的出现是以长寿命的湍流的形式表示的，该湍流在很长一段时间内保持在“准平衡”状态。最重要的是，这种自组织行为的不可逆混合的结果似乎是其特征一般由一个通用的累积湍流通量系数$Γ_c \sim 0.2$只为湍流所产生的Holmboe波不稳定性。这种自组织临界状态的存在证实了与分层湍流的自调节有关的原始物理论点，正如Turner（1973）所描述的那样，它涉及一种“平衡”。
英文摘要：
Motivated by the importance of stratified shear flows in geophysical and environmental circumstances, we characterize their energetics, mixing and spectral behavior 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-organised 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 localisation of the `scouring' motions (i.e. `avalanches') that are characteristic of the turbulence induced by the break down 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 localised `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-organised behavior appears to be characterized generically by a universal cumulative turbulent flux coefficient of $Γ_c \sim 0.2$ only for turbulent flows engendered by Holmboe wave instability. The existence of this self-organised 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).
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