Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?
Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?
复制标题
地球物理流中剪切引起的混合：湍流的路径对其效率是否重要？
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;W. Peltier
本文从大尺度海洋环流模式中日混合参数化的重要性出发，详细分析了密度分层切变流中的高雷诺数混合，它构成了海洋内部控制湍流扩散的小尺度物理过程的典型例子。我们的重点是关于分层混合层中达到充分发展的湍流的路径是否在任何重要的方式上决定了由有效湍流扩散率表示的日混合效率。我们通过初级开尔文-亥姆霍兹巨流通过次级不稳定的性质来描述到完全发展的湍流的不同路径，以执行到这种状态的转变。然后，我们证明了不同的湍流转换机制，在这些不同的转换机制中，导致日周期混合效率和有效浮力垂直通量的值有很大的不同。我们指出，基于实验室测量和类似的低雷诺数数值模拟，剪切诱导层状湍流混合效率的普遍取值0.15-0.2对于地球物理流动的高雷诺数区域特征来说可能太低了。我们的结果表明，对于足够大的雷诺数，当Richardson数的中间值为0.12时，混合效率趋于1/3美元。这与考尔菲尔德、唐和普林德(《流体力学》，第498卷，2004年，第315-332页)关于分层Couette流混合效率的渐近值的理论预测是一致的。在高雷诺数区域，在特定的剪切诱导混合过程中，混合效率在相当大的范围内变化。我们基于对潜在动力的详细检查来解释这种变化。由于混合效率在0.15-0.2范围内的值已被广泛用于从海洋微结构测量和全球海洋环流要求的能量平衡分析中推断有效扩散系数，我们的发现对大规模海洋模拟具有潜在的重要意义。我们还量化了采用Osborne(J.Phys.《海洋》，第10卷，1980年，第83-89页)公式以及0.15的效率来推断有效扩散系数的值，并解释这一结论的逻辑基础。从我们对分层湍流的理论理解的角度来看，这项工作的一个更重要的方面是证明了能量的逆级联被雷诺数增加到地球物理流动的典型值而强烈地抑制，而这种逆级联是由实验室实验和剪切流演化的低雷诺数模拟中典型的涡合过程所促进的。基于这一发现，需要重新考虑将基于低雷诺数(数值或实验室)实验的结果应用于高雷诺数地球物理剪切流。
Abstract Motivated by the importance of diapycnal mixing parameterizations in large-scale ocean general circulation models, we provide a detailed analysis of high-Reynolds-number mixing in density stratified shear flows which constitute an archetypical example of the small-scale physical processes occurring in the oceanic interior that control turbulent diffusion. Our focus is upon the issue as to whether the route to fully developed turbulence in the stratified mixing layer is in any significant way determinant of diapycnal mixing efficiency as represented by an effective turbulent diffusivity. We characterize different routes to fully developed turbulence by the nature of the secondary instabilities through which a primary Kelvin–Helmholtz billow executes the transition to this state. We then demonstrate that different mechanisms of turbulence transition characterized in these different transition mechanisms lead to considerably different values for the efficiency of diapycnal mixing and also for the effective vertical flux of buoyancy. We show that the widely employed value of 0.15–0.2 for the efficiency of mixing in shear-induced stratified turbulence based upon both laboratory measurements and similarly low-Reynolds-number numerical simulations may be too low for the high-Reynolds-number regime characteristic of geophysical flows. Our results show that the mixing efficiency tends to a value of approximately $1/ 3$ for sufficiently large Reynolds number at an intermediate value of 0.12 for the Richardson number. This is in agreement with a theoretical predictions of Caulfield, Tang and Plasting (J. Fluid Mech., vol. 498, 2004, pp. 315–332) for the asymptotic value of mixing efficiency in stratified Couette flows. In the high-Reynolds-number regime, mixing efficiency is shown to vary over a considerable range during the course of a particular shear-induced mixing event. We explain this variation on the basis of a detailed examination of the underlying dynamics. Since values in the range 0.15–0.2 for mixing efficiency have been extensively employed to infer an effective diffusivity from ocean microstructure measurements and also in energy balance analyses of the requirements of the global ocean circulation, our findings have potentially important implications for large-scale ocean modelling. We also quantify the errors introduced by employing the Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) formula along with an efficiency of 0.15 to infer values for effective diffusivity, and explain the logical underpinnings of this conclusion. One of the more important aspects of this work from the perspective of our theoretical understanding of stratified turbulence is the demonstration that the inverse cascade of energy, which is facilitated by the vortex-merging process that is typical of laboratory experiments and of the low-Reynolds-number simulations of shear flow evolution, is strongly suppressed by increase of the Reynolds number to values typical of geophysical flows. Based on this finding, the application of results based on low-Reynolds-number (numerical or laboratory) experiments to high-Reynolds-number geophysical shear flows needs to be reconsidered.