Viscoelastic plane Poiseuille flow is shown to become linearly unstable in the absence of inertia, in the limit of high elasticities, for ultradilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues up to a Reynolds number (Re) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultradilute polymer solutions, a single linearly unstable modal branch may underlie transition to elastic turbulence at zero Re and to elasto-inertial turbulence at moderate Re, implying the existence of continuous pathways connecting the turbulent states to each other and to the laminar base state.

中文翻译：

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粘弹性通道流中弹性-惯性和弹性湍流状态之间的连续通路

对于超稀聚合物溶液，在没有惯性的情况下，在高弹性的限制下，粘弹性平面泊肃叶流会变得线性不稳定。虽然已经预测了曲线剪切流的无惯性弹性不稳定性，但这是有史以来第一次报告直线剪切流中的纯弹性线性不稳定性。新的不稳定性持续到雷诺数 (Re) 为$哦(1000)$，对应于最近确定的弹性惯性湍流状态，该状态被认为是最大减阻机制的基础。因此，对于高弹性的超稀聚合物溶液，单个线性不稳定模态分支可能是向零 Re 时的弹性湍流和中等 Re 时的弹性惯性湍流过渡的基础，这意味着存在将湍流状态相互连接并与层流基态。