Secondary instability of a temporally growing mixing layer
Secondary instability of a temporally growing mixing layer
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DOI：
10.1017/s0022112087002866
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发表时间：
1987-11
影响因子：
3.7
通讯作者：
R. Metcalfe;S. Orszag;M. Brachet;S. Menon;J. Riley
中科院分区：
文献类型：
--
作者：
R. Metcalfe;S. Orszag;M. Brachet;S. Menon;J. Riley
本文用直接数值积分的方法研究了平面混合层二维涡态的三维稳定性。小尺度的不稳定性存在的展向尺度在经典的线性模式是稳定的。这些模式的增长对流的时间尺度，提取其能量的平均流量和存在于适度低雷诺数。它们的增长率与增长最快的无粘不稳定性和二维次谐波（配对）模式的增长率相当。在高振幅下，它们可以演变成成对的反向旋转的流向涡，连接主展向涡，这与实验室实验中观察到的结构非常相似。的三维模式不出现饱和在准稳态的情况下，在没有配对的情况下，纯二维的基本和次谐波模式。流动的后续演变取决于成对模式的相对振幅。持久的配对可以抑制三维不稳定性，因此，保持流动主要是二维的。相反，抑制配对过程可以将三维模式驱动到更混乱的、类似顺从的状态。充分湍流混合层的高分辨率模拟的分析证实了肋状结构的存在，它们的相干性强烈依赖于二维配对模式的存在。
The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.