Degeneracy of turbulent states in two-dimensional channel flow
Degeneracy of turbulent states in two-dimensional channel flow
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DOI：
10.1017/jfm.2021.336
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发表时间：
2021-05
影响因子：
3.7
通讯作者：
Vilda K. Markeviciute;R. Kerswell
中科院分区：
文献类型：
--
作者：
Vilda K. Markeviciute;R. Kerswell
摘要：本文通过直接数值模拟重新研究了雷诺数为$Re\in[7000,72\ 000]$时具有固定体积通量的二维通道流动，并揭示了湍流状态的多重稳定性区域。当$Re \in[21\,000, 42\ 000]$与已知的对称解（$2h$是通道高度，$U$是平均流速）相邻时，新的不对称状态（基于比较每个通道壁上的时间平均平均剪切）至少存在$32\,000\,h/U$。对称和非对称状态都类似于行波，甚至在Re=5772$处的初始分叉处的Re$一个数量级以上，而非对称状态在其中一个通道壁上表现出加剧的湍流行为。与对称状态相比，这些不对称状态的压力梯度降低了22%。两个视吸引子之间的鞍态是由初级分岔产生的行波解。到$Re=43\ 000$时，对称解变得不稳定，只留下非对称态及其反射对偶作为吸引子，直到至少$Re=46\,875$。在$Re=60\ 000$时，这对非对称状态连接起来，使得“湍流”壁明显地随机而不频繁地切换。以这种方式，流的对称性然后恢复，但只有在非常长的时间（$\gg 10^5 h/U$）平均之后。
Abstract We revisit two-dimensional channel flow with fixed volume flux for Reynolds numbers $Re\in [7000,72\,000]$ via direct numerical simulations and uncover a region of multistability of turbulent states. New asymmetric states (based on comparing the time-averaged mean shear on each of the channel walls) exist for at least $32\,000\,h/U$ when $Re \in [21\,000, 42\,000]$ alongside the known symmetric solution ($2h$ is the channel height and $U$ is the mean flow rate). Both the symmetric and asymmetric states resemble a travelling wave even at $Re$ an order of magnitude above the primary bifurcation at $Re=5772$ with the asymmetric state showing heightened turbulent behaviour near one of the channel walls. These asymmetric states display up to $22\,\%$ reduction in pressure gradient compared with their symmetric counterparts. The saddle state between the two apparent attractors is shown to be the travelling wave solution which originates from the primary bifurcation. By $Re=43\,000$, the symmetric solution has become unstable leaving only the asymmetric state and its reflected counterpart as attractors until at least $Re=46\,875$. At $Re=60\,000$, the pair of asymmetric states become connected so that the ‘turbulent’ wall switches apparently randomly and infrequently. In this way, the symmetry of the flow is then restored but only after averaging over extremely long times ($\gg 10^5 h/U$).