How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=\rho v_0^2/2{\sigma }_a$, where $\rho$ is the suspension mass density, $v_0$ the swim speed, and ${\sigma }_a$ the active stress. Linear stability analysis shows that, for small $R$, disturbances grow at a rate linear in their wave number $q$ and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity, we find a slower growth rate, of $O(q^2)$; the numerically observed steady state is phase turbulent: noisy but aligned on average. We present numerical evidence in three and two dimensions that this inertia-driven flocking transition is continuous, with a correlation length that grows on approaching the transition. For much larger $R$, we find an aligned state linearly stable to perturbations at all $q$. Our predictions should be testable in suspensions of mesoscale swimmers [, Soft Matter 15, 8946 (2019)].

中文翻译：

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惯性驱动粘性活性流体中的植绒相变

一群有方向的可伸展游泳者必须游多快才能摆脱粘性主动悬浮液的不稳定性？我们证明答案在于无量纲组合$\mathrm{电阻}=\rho v_0^2/2{\sigma }_{\mathrm{一种}}$， 在哪里 $\rho$ 是悬浮质量密度， $v_0$ 游泳速度，以及 ${\sigma }_{\mathrm{一种}}$主动应力。线性稳定性分析表明，对于小$\mathrm{电阻}$, 扰动以其波数线性增长 $q$并且主要的不稳定模式涉及扭曲。在我们的数值研究中产生的稳态是各向同性刺猬缺陷湍流。过了第一关$\mathrm{电阻}$ 秩序统一，我们发现一个较慢的增长率， $哦(q^2)$; 数值观察到的稳态是相位湍流：嘈杂但平均对齐。我们提供了三个和两个维度的数值证据，表明这种惯性驱动的植绒过渡是连续的，相关长度随着接近过渡而增长。对于更大的$\mathrm{电阻}$，我们发现对齐状态对扰动完全线性稳定 $q$. 我们的预测应该可以在中尺度游泳者的悬浮中进行测试 [, Soft Matter 15 , 8946 (2019)]。