This work employs invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on Nagata's upper-branch equilibrium solution at low Reynolds numbers where this solution is linearly stable. When adding a single heavy particle with a diameter equivalent to 2.5 wall units ($\frac{1}{12}$ of the gap width), we observe that the solution remains stable and is essentially unchanged away from the particle. This result demonstrates that it is technically feasible to utilize exact coherent structures in conjunction with particle-resolved direct numerical simulation. While translating in the streamwise direction, the particle migrates laterally under the action of the quasistreamwise vortices until it reaches the region occupied by the low-speed streak, where it attains a periodic state of motion, independent of its initial position. As a result of the ensuing preferential particle location, the time-average streamwise particle velocity differs from the plane-average fluid-phase velocity at the same wall distance as the particle center, as previously observed in experiments and in numerical data for fully turbulent wall-bounded flows. Additional constrained simulations where the particle is maintained at a fixed spanwise position while freely translating in the other two directions reveal the existence of two equilibria located in the low-speed and the high-speed streak, respectively, the former being an unstable point. A parametric study with different particle to fluid density ratios is conducted which shows how inertia affects the spanwise fluctuations of the periodic particle motion. Finally, we discuss a number of potential future investigations of solid particle dynamics which can be conducted with the aid of invariant solutions (exact coherent structures) of the Navier-Stokes equations.

中文翻译：

---

可以借助平衡解来再现平面Couette湍流中有限尺寸颗粒的优先浓度吗？

这项工作采用了Navier-Stokes方程的不变解来研究有限尺寸粒子与近壁相干结构之间的相互作用。我们考虑水平面库埃特流，并集中在低雷诺数下永田的上分支平衡解，该解线性稳定。当添加直径等于2.5个壁单元的单个重颗粒时（$\frac{\mathrm{1个}}{12}$间隙宽度的变化），我们观察到溶液保持稳定，并且远离颗粒基本上没有变化。该结果表明，结合精确的相干结构和粒子解析直接数值模拟在技术上是可行的。当沿流向平移时，粒子在准流向涡旋的作用下横向迁移，直到到达低速条纹所占据的区域，并在那里获得周期性的运动状态，而与初始位置无关。作为随后优先粒子定位的结果，在与粒子中心相同的壁距处，时间平均流向粒子速度不同于平面平均流体相速度，如先前在实验和在全湍流壁的数值数据中观察到的那样界流。额外的约束模拟将粒子保持在固定的展向位置，同时在其他两个方向上自由移动，这揭示了分别存在于低速和高速条纹中的两个平衡点，前者是不稳定点。进行了具有不同粒子与流体密度比的参数研究，该研究显示了惯性如何影响周期性粒子运动的翼展方向波动。最后，我们讨论了固体粒子动力学的许多潜在的未来研究，这些研究可以借助Navier-Stokes方程的不变解（精确的相干结构）进行。