Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence
Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence
复制标题
浮力主导的分层湍流中不稳定周期轨道的不可逆混合
DOI：
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发表时间：
2017
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：
D. Lucas;Colm‐cille P. Caulfield
我们考虑在Kolmogorov流动中由大规模水平切变驱动的湍流（即正弦体强迫）和具有浮力频率的背景线性稳定分层 $N_{B}^{2}$ 施加在第三，垂直方向上的流体与运动粘度 $\unicode[STIX]{x1D708}$ ． 众所周知，这种流动被非线性不稳定的稳定状态组织成层，在垂直方向上倾斜背景切变，可以证明是一系列不稳定的有限振幅饱和，最初来自层流状态。在这里，我们研究了该系统中的下一个运动顺序，即密度场不可逆混合的时间依赖机制。这项调查是通过“循环流分析”来实现的。我们确定（不稳定的）周期轨道，嵌入在湍流吸引子中，并使用这些轨道作为混沌流的代理。我们发现，流动的“混合效率”的适当度量的时间平均值 $\mathscr{E}=\unicode[STIX]{x1D712}/(\unicode[STIX]{x1D712}+{\mathcal{D}})$ (哪里 ${\mathcal{D}}$ 体积平均动能耗散率和 $\unicode[STIX]{x1D712}$ 体积平均密度方差耗散率是否随时间平均浮力雷诺数非单调变化 $\overline{Re}_{B}=\overline{{\mathcal{D}}}/(\unicode[STIX]{x1D708}N_{B}^{2})$ ，上面有 $1/6$ ，与奥斯本的经典模型一致（J.物理学）。Oceanogr，第10卷(1)，1980年，第83-89页)。在不可逆混合效率较低的不稳定轨道之间存在着质的不同 $\overline{Re}_{B}\sim O(1)$ 以及那些接近最优的 $\mathscr{E}\lesssim 1/6$ 中级 $\overline{Re}_{B}\sim 10$ ． 较弱的轨道不可避免地嵌入更强的分层流中，其特征是紧张或“冲刷”运动，而更有效的轨道在更弱的分层流中具有明显的倾覆动力学，并且明显是剪切不稳定的流动。
We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency $N_{B}^{2}$ imposed in the third, vertical direction in a fluid with kinematic viscosity $\unicode[STIX]{x1D708}$ . This flow is known to be organised into layers by nonlinear unstable steady states, which incline the background shear in the vertical and can be demonstrated to be the finite-amplitude saturation of a sequence of instabilities, originally from the laminar state. Here, we investigate the next order of motions in this system, i.e. the time-dependent mechanisms by which the density field is irreversibly mixed. This investigation is achieved using ‘recurrent flow analysis’. We identify (unstable) periodic orbits, which are embedded in the turbulent attractor, and use these orbits as proxies for the chaotic flow. We find that the time average of an appropriate measure of the ‘mixing efficiency’ of the flow $\mathscr{E}=\unicode[STIX]{x1D712}/(\unicode[STIX]{x1D712}+{\mathcal{D}})$ (where ${\mathcal{D}}$ is the volume-averaged kinetic energy dissipation rate and $\unicode[STIX]{x1D712}$ is the volume-averaged density variance dissipation rate) varies non-monotonically with the time-averaged buoyancy Reynolds numbers $\overline{Re}_{B}=\overline{{\mathcal{D}}}/(\unicode[STIX]{x1D708}N_{B}^{2})$ , and is bounded above by $1/6$ , consistently with the classical model of Osborn (J. Phys. Oceanogr., vol. 10 (1), 1980, pp. 83–89). There are qualitatively different physical properties between the unstable orbits that have lower irreversible mixing efficiency at low $\overline{Re}_{B}\sim O(1)$ and those with nearly optimal $\mathscr{E}\lesssim 1/6$ at intermediate $\overline{Re}_{B}\sim 10$ . The weaker orbits, inevitably embedded in more strongly stratified flow, are characterised by straining or ‘scouring’ motions, while the more efficient orbits have clear overturning dynamics in more weakly stratified, and apparently shear-unstable flow.
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DOI：
10.17863/cam.9670
发表时间：
2017
期刊：
--
影响因子：
--
作者：
Caulfield C
通讯作者：
Caulfield C
影响因子：
4.6
作者：
D. Lucas;R. Kerswell
通讯作者：
D. Lucas;R. Kerswell
影响因子：
3.7
作者：
Lucas D
通讯作者：
Lucas D
水平强制分层湍流中的层形成：将精确的相干结构与线性不稳定性联系起来
影响因子：
3.7
作者：
Lucas D
通讯作者：
Lucas D
影响因子：
3.7
作者：
Chandler, Gary J.;Kerswell, Rich R.
通讯作者：
Kerswell, Rich R.