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Lagrangian structures and mixing in the wake of a streamwise oscillating cylinder

机译：拉格朗日结构和流向振荡圆柱后的混合

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摘要

Lagrangian analysis is capable of revealing the underlying structure and complex phenomena in unsteady flows. We present particle-image velocimetry measurements of the wake of a cylinder undergoing streamwise vortex-induced vibrations and calculate the Finite-Time Lyapunov Exponents (FTLE) in backward-and forward-time. The FTLE fields are compared to the phase-averaged vorticity fields for the four different wake modes observed while the cylinder experiences streamwise vortex-induced vibrations. The backward-time FTLE fields characterise the formation of vortices, with the roll up of spiral-shaped ridges coinciding with the roll up of the shear layers to form the vortices. Ridges in the forward-time fields tend to lie perpendicular to the flow direction and separate nearby vortices. The shedding of vortices coincides with a "peel off" process in the forward-time FTLE fields, in which a ridge connected to the cylinder splits into two strips, one of which moves downstream. Particular attention is given to the "wake breathing" process, in which the streamwise motion of the cylinder causes both shear layers to roll up simultaneously and two vortices of opposite sign to be shed into the wake. In this case, the ridges in forward-time FTLE fields are shown to define "vortex cells," in which the new vortices form, and the FTLE fields allow the wake to be decomposed into three distinct regions. Finally, the mixing associated with each wake mode is examined, and it is shown that cross-wake mixing is significantly enhanced when the vibration amplitude is large and the vortices are shed alternately. However, while the symmetric shedding induces large amplitude vibrations, no increase in mixing is observed relative to the von Karman vortex street observed behind near-stationary bodies. (C) 2016 Author(s).
机译：拉格朗日分析能够揭示不稳定流中的潜在结构和复杂现象。我们提出了一个圆柱流尾流的粒子图像测速仪测量，该圆柱流受到流向涡流诱发的振动，并计算了向前和向后时间的有限时间李雅普诺夫指数（FTLE）。将FTLE场与观察到的四种不同尾流模式的相位平均涡度场进行比较，同时观察圆柱体沿流向涡流引起的振动。倒时FTLE场表征了涡旋的形成，螺旋形脊的卷积与剪切层的卷积相吻合，形成了涡旋。前向时间场中的山脊往往垂直于流向，并分开附近的涡流。旋涡的脱落与正向FTLE场中的“剥离”过程相吻合，在该过程中，连接到圆柱体的山脊分成两个条带，其中一条向下游移动。特别注意“尾流呼吸”过程，其中，圆柱体沿流向运动会导致两个剪切层同时滚动，并使两个相反符号的涡旋掉入尾流。在这种情况下，前向FTLE字段中的脊将显示为定义“涡流单元”，在其中形成新的涡流，而FTLE字段允许将尾流分解为三个不同的区域。最后，检查了与每个唤醒模式相关的混合，并且显示出，当振动幅度较大且涡旋交替掉落时，交叉唤醒混合得到显着增强。但是，尽管对称脱落引起大振幅振动，但相对于在近静止物体后面观察到的von Karman涡街，没有观察到混合增加。 （C）2016作者。

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