Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux
Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux
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分层湍流剪切流中的时间依赖性非单调混合：对浮力通量海洋学估计的影响
DOI：
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发表时间：
2013
影响因子：
3.7
通讯作者：
W. Peltier
中科院分区：
文献类型：
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作者：
A. Mashayek;Colm‐cille P. Caulfield;W. Peltier
本文采用直接数值模拟的方法，研究了体积Richardson数在$0范围内的稳定分层自由剪切层中切变诱导湍流的日混合效率。12\leq R{i}_{0}\leq 0。2$，雷诺数$Re=6000$。结果表明，混合效率非单调地依赖于{R{i}{0}$，在0.14-0.16范围内达到峰值，这与浮力通量和耗散率都达到最大值的范围非常吻合。通过对流动演化的能量学和基本动力学的详细分析，我们证明了在0美元范围内存在高混合效率。14\lt R{i}_{0}\lt 0。16美元是由于出现了大量的小尺度不稳定，这些不稳定在较低的理查森数时不存在，但在较高的理查森数时稳定下来。正如Mashayek和Peltier(J.Fluid Mech，Vol.725,2013，pp.216-261)中所讨论的，只有当雷诺数高于一个临界值时，才能实现在中等Richardson数下存在如此多的二次不稳定以及随后的高混合效率，该临界值通常高于实验室环境中可达到的临界值，以及先前大多数剪切诱导分层湍流的数值研究中所达到的临界值。我们进一步证明了被广泛使用的奥斯本(J.Phys.大洋洲。第10卷，1980年，第83-89页)公式是基于的，以及它的对应物和导数，通过一个(恒定)通量系数($\Gamma$)将浮力通量与耗散率联系起来，在较高的Richardson数下失效，只要雷诺数足够高。具体地说，我们证明了完全发展、定常和各向同性湍流的假设在高Richardson数时都失效了。结果表明，当Richardson数大于与最大混合效率对应的Richardson数时，这些假设的崩溃最为显著，这一事实突出了混合效率对Richardson数的非单调性的重要性，我们认为这是分层剪切诱导湍流的特征。在高R值时，湍流的生命周期由一个快速增长期和一个快速衰减期组成。在整个生命周期中，在小尺度湍流和较大相干结构之间存在着相当大的能量交换，这些结构在流动演化的不同阶段中幸存下来。由于切变不稳定是在数百米以下和海洋不同深度的湍流能量耗散的最主要机制之一，我们的结果对于根据海洋环境中微结构测量来推断湍流扩散率具有重要的意义。
Abstract We employ direct numerical simulation to investigate the efficiency of diapycnal mixing by shear-induced turbulence in stably stratified free shear layers for flows with bulk Richardson numbers in the range $0. 12\leq R{i}_{0} \leq 0. 2$ and Reynolds number $Re= 6000$ . We show that mixing efficiency depends non-monotonically upon $R{i}_{0} $ , peaking in the range 0.14–0.16, which coincides closely with the range in which both the buoyancy flux and the dissipation rate are maximum. By detailed analyses of the energetics of flow evolution and the underlying dynamics, we show that the existence of high mixing efficiency in the range $0. 14\lt R{i}_{0} \lt 0. 16$ is due to the emergence of a large number of small-scale instabilities which do not exist at lower Richardson numbers and are stabilized at high Richardson numbers. As discussed in Mashayek & Peltier (J. Fluid Mech., vol. 725, 2013, pp. 216–261), the existence of such a well-populated ‘zoo’ of secondary instabilities at intermediate Richardson numbers and the subsequent high mixing efficiency is realized only if the Reynolds number is higher than a critical value which is generally higher than that achievable in laboratory settings, as well as that which was achieved in the majority of previous numerical studies of shear-induced stratified turbulence. We furthermore show that the primary assumptions upon which the widely employed Osborn (J. Phys. Oceanogr. vol. 10, 1980, pp. 83–89) formula is based, as well as its counterparts and derivatives, which relate buoyancy flux to dissipation rate through a (constant) flux coefficient ( $\Gamma $ ), fail at higher Richardson numbers provided that the Reynolds number is sufficiently high. Specifically, we show that the assumptions of fully developed, stationary, and isotropic turbulence all break down at high Richardson numbers. We show that the breakdown of these assumptions occurs most prominently at Richardson numbers above that corresponding to the maximum mixing efficiency, a fact that highlights the importance of the non-monotonicity of the dependence of mixing efficiency upon Richardson number, which we establish to be characteristic of stratified shear-induced turbulence. At high $R{i}_{0} $ , the lifecycle of the turbulence is composed of a rapidly growing phase followed by a phase of rapid decay. Throughout the lifecycle, there is considerable exchange of energy between the small-scale turbulence and larger coherent structures which survive the various stages of flow evolution. Since shear instability is one of the most prominent mechanisms for turbulent dissipation of energy at scales below hundreds of metres and at various depths of the ocean, our results have important implications for the inference of turbulent diffusivities on the basis of microstructure measurements in the oceanic environment.