The structure and origin of confined Holmboe waves
The structure and origin of confined Holmboe waves
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DOI：
10.1017/jfm.2018.324
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发表时间：
2018-06-05
影响因子：
3.7
通讯作者：
Linden, P. F.
中科院分区：
文献类型：
--
作者：
Lefauve, Adrien;Partridge, J. L.;Linden, P. F.
分层剪切流不稳定性的有限振幅表现及其时空相干结构被认为在湍流地球物理流中发挥着重要作用。这种剪切流通常具有由尖锐的密度界面分隔的层，因此容易受到所谓的霍尔姆布不稳定性及其有限振幅表现形式——霍尔姆布波的影响。在本文中，我们描述并阐明了实验室中通过连接两个充满不同密度流体的倾斜方形管道的交换流产生的持续分层剪切流中明显先前未报道的长寿命相干结构的起源。使用一种新颖的测量技术，可以在三维体积上同时对三分量速度和密度场进行时间分辨、近乎瞬时的测量，我们描述了该结构的三维几何和时空动力学。我们将其识别为有限振幅、非线性、不对称受限 Holmboe 波 (CHW)，并强调了其受管道边界的展向（横向）限制的重要性。我们特别关注展向涡度，它表现出一种移动的、近周期的剪切、扭曲、长球体结构，具有较宽的“bodya epsilon(TM)”和较窄的“heada epsilon(TM)”。通过对二维流向平均实验流进行时间线性稳定性分析，我们求解了具有二维横截面限制本征函数和流向法向模式的三维扰动。我们表明，增长最快的受限 Holmboe 不稳定性的色散关系和三维空间结构与观测到的受限 Holmboe 波非常一致。我们还将这些结果与一维基流的二维扰动（即没有展向依赖性）的经典线性分析进行比较。我们的结论是，横向约束是约束 Holmboe 不稳定性的重要组成部分，它会产生 CHW，对许多固有约束的地球物理流（如山谷、河口、海峡或深海海沟）产生影响。我们的结果表明，CHW 是一个实验观察到的、本质上非线性的、鲁棒的、长寿命的相干结构的例子，它是从线性不稳定性发展而来的。我们推测，CHW 是一类精确相干态的有希望的候选者，这些态支撑着更加无序但持续强制的分层剪切流的动力学。
Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ' bodya epsilon(TM) and a narrower ' heada epsilon(TM). Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.