使用罕见事件算法捕获的过渡壁turbulence塌陷
Collapse of transitional wall turbulence captured using a rare events algorithm
摘要：
本文介绍了第一个成功的应用罕见事件方法的研究多稳定性的湍流无随机能量注入。本文用\emph{Adaptive Multilevel Splitting}（AMS）系统地计算了平面Couette流中湍流崩溃的轨迹及其发生的概率和速率。AMS计算在尺寸为$L_x\times L_z=24\times 18$的系统中进行，雷诺数为$R=370$，相对于DNS加速度为因子$\mathcal{O}(10)$;在尺寸为$L_x\times L_z=36\times 27$的系统中进行，雷诺数为$R=377$，加速度为因子$\mathcal{O}(10^3)$。AMS的结果进行了验证与DNS的大小$L_x\times L_z=24\times 18$的系统中的比较。这两个系统的可视化都表明，湍流的崩溃是因为湍流的自我维持过程局部失败。流向涡首先在流向细长孔中衰减，留下经历粘性衰减的流向不变的流向速度管。然后这些孔沿翼展方向延伸。在尺寸为$L_x\times L_z=24\times 18$的系统中，对$(E_{c,x}=\int u_x^2/2\,{\rm d}^3\mathbf{x},E_{c,y-z}=\int (u_y^2/2+u_z^2/2)\,{\rm d}^3\mathbf{x})$平面上的一千多条轨迹的检查证实了流向涡的衰减更快，并显示了轨迹的集中。这暗示了大尺寸极限下的瞬子现象。转折点状态的计算，超过该laminarisation是肯定的，确认了孔形成的情况下，并表明，它是更明显的在较大的系统。最后，非反应轨迹的检查，孔打开，然后关闭，表明孔打开和关闭是不同的过程。当层流孔关闭时，涡和条纹都随之重新形成。
英文摘要：
This text presents one of the first successful applications of a rare events method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow, as well as their probability and rate of occurrence are systematically computed using \emph{Adaptive Multilevel Splitting} (AMS). The AMS computations are performed in a system of size $L_x\times L_z=24\times 18$ at Reynolds number $R=370$ with an acceleration by a factor $\mathcal{O}(10)$ with respect to DNS and in a system of size $L_x\times L_z=36\times 27$ at Reynolds number $R=377$ with an acceleration by a factor $\mathcal{O}(10^3)$. The AMS results are validated with a comparison to DNS in the system of size $L_x\times L_z=24\times 18$. Visualisations in both systems indicate that turbulence collapses because the self sustaining process of turbulence fails locally. The streamwise vortices decay first in streamwise elongated holes, leaving streamwise invariant streamwise velocity tubes that experience viscous decay. These holes then extend in the spanwise direction. The examination of more than a thousand of trajectories in the $(E_{c,x}=\int u_x^2/2\,{\rm d}^3\mathbf{x},E_{c,y-z}=\int (u_y^2/2+u_z^2/2)\,{\rm d}^3\mathbf{x})$ plane in the system of size $L_x\times L_z=24\times 18$ confirms the faster decay of streamwise vortices and shows concentration of trajectory. This hints at an instanton phenomenology in the large size limit. The computation of turning point states, beyond which laminarisation is certain, confirms the hole formation scenario and shows that it is more pronounced in larger systems. Finally, the examination of non reactive trajectories, where a hole opens then closes, indicates that hole opening and closing are distinct processes. Both the vortices and the streaks reform concomitantly when the laminar holes close.
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