The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ( $Re$ ) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

中文翻译：

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惯性弹性湍流 Taylor-Couette 流的直接数值模拟

惯性弹性湍流 Taylor-Couette 流的流动物理特性 $0.5$ 在雷诺数 ( $重新$ ） 范围 500 美元 到 $8000$ 通过直接数值模拟进行研究。结果表明，作为 $重新$ 增加的湍流动力学可以细分为两种不同的状态：（i）低 $Re \leqslant 1000$ 流动物理学主要由非线性弹性力主导的状态，对动量、应力和能量的传输和混合的主要贡献来自主体区域中的大规模流动结构和（ii）高 $Re \geqslant 5000$ 惯性力控制流动物理的机制，流动动力学主要由近壁区域的小尺度流动结构控制。流动-微观结构耦合分析表明，近壁区域的弹性 Görtler 不稳定性是通过显着的聚合物延伸和相应的高环向应力触发的。这种不稳定性导致小尺度弹性涡旋结构被识别为弹性 Görtler 涡旋，这些涡旋完全存在 $重新$ 经过考虑的。事实上，这些涡旋在内壁附近形成人字形条纹，由于它们的弹性起源，它们的平均寿命比牛顿对应物更长。检查平均流向熵、平均动能、湍流动能和雷诺剪应力的预算表明，增加流体惯性会阻碍弹性应力的产生，导致弹性相关效应对流动物理的影响单调减少。