论文标题
粘弹性通道中的有限振幅弹性波从较大到零雷诺数
Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
论文作者
论文摘要
使用Fene-P模型中的分支延续，我们表明，粘弹性通道流的最近发现的线性不稳定性（Khalid等人{\ em J. {\ em J.流动性机械} {\ bf 915}，A43，2021）的中等程度比Wiissenberg（$ WI） Reynolds（$ re $）数字超过$ re \ in [0,3000] $。下部分支上的行进波非常弱，表明粘体通道流动容易受到$ Wi $的小有限幅度干扰触发的（非线性）不稳定性，而$ re $ $ $ $均低于中性曲线。这些波浪中出现在马鞍节点分叉中的关键$ Wi $单调降低，例如，$ \ 37 $ at $ re re = 3000 $ = 3000 $降低到$ \ $ \ $ \ y = 0 $ = 0 $，在溶剂到total-total-total-total-total-total-total-total-viscosity-viscosity-viscosity-viscosity $β= 0.9 $ = 0.9 $。在后一个爬行的流量极限中，我们还表明，这些波的存在于$ Wi \ Lessim 50 $，用于更高的聚合物浓度 - $β\ in [0.5,0.97）$ - 在没有已知的线性不稳定的情况下。因此，我们的结果表明，这些行进波 - 在模拟中发现，并由Dubief等人命名为“箭头”。 {\ em arxiv} .2006.06770（2020） - 比$（Wi，re，β）$参数空间更普遍地存在于其产卵中性曲线，因此可以直接或间接通过其不稳定性，从而影响其远离线性不稳定的动态。讨论了与弹性和弹性惯性湍流的可能连接。
Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently-discovered linear instability of viscoelastic channel flow (Khalid et al. {\em J. Fluid Mech.} {\bf 915}, A43, 2021) are substantially subcritical reaching much lower Weissenberg ($Wi$) numbers than on the neutral curve at a given Reynolds ($Re$) number over $Re \in [0,3000]$. The travelling waves on the lower branch are surprisingly weak indicating that viscolastic channel flow is susceptible to (nonlinear) instability triggered by small finite amplitude disturbances for $Wi$ and $Re$ well below the neutral curve. The critical $Wi$ for these waves to appear in a saddle node bifurcation decreases monotonically from, for example, $\approx 37$ at $Re=3000$ down to $\approx 7.5$ at $Re=0$ at the solvent-to-total-viscosity ratio $β=0.9$. In this latter creeping flow limit, we also show that these waves exist at $Wi \lesssim 50$ for higher polymer concentrations - $β\in [0.5,0.97)$ -- where there is no known linear instability. Our results therefore indicate that these travelling waves -- found in simulations and named `arrowheads' by Dubief et al. {\em arXiv}.2006.06770 (2020) - exist much more generally in $(Wi,Re, β)$ parameter space than their spawning neutral curve and hence can either directly, or indirectly through their instabilities, influence the dynamics seen far away from where the flow is linearly unstable. Possible connections to elastic and elasto-inertial turbulence are discussed.
