Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number Re = 3000 reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien-Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a new solution family that is nonlinearly self-sustained by viscoelasticity. The ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear TS mode, and increases strongly with Weissenberg number, Wi. For the latter, there is a transition in the scaling of this ratio as Wi increases, and the Wi at which the nonlinear solution family comes into existence is just above this transition. Finally, evidence indicates that this branch is connected through an unstable solution branch to two-dimensional elastoinertial turbulence (EIT). These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the Tollmien-Schlichting mode.

中文翻译：

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自持弹性惯性 Tollmien-Schlichting 波

雷诺数 Re = 3000 时粘弹性流体的二维平面通道流动的直接模拟揭示了一系列吸引子的存在，其结构与线性 Tollmien-Schlichting (TS) 模式非常相似，特别是在TS 模式的临界层位置。在选定的参数值下，该求解分支没有连接到为牛顿流找到的非线性 TS 求解分支，因此代表了一个新的解决方案族，它由粘弹性非线性自维持。对于吸引子和线性 TS 模式，应力和速度波动之间的比率在定量上一致，并且随着魏森伯格数 Wi 的增加而强烈增加。对于后者，随着 Wi 的增加，该比率的缩放会发生变化，非线性解决方案族出现时的 Wi 刚好在此过渡之上。最后，有证据表明该分支通过不稳定解分支连接到二维弹性惯性湍流 (EIT)。这些结果表明，在此处考虑的参数范围内，导致 EIT 的旁路过渡是由激发 Tollmien-Schlichting 模式的扰动的非线性放大和自维持介导的。