[论文解读] Subcritical route to turbulence via the Orr mechanism in a quasi-two-dimensional boundary layer

Christopher J. Camobreco, Alban Pothérat+1 more|arXiv (Cornell University)|Nov 19, 2020

Fluid Dynamics and Turbulent Flows参考文献 64被引用 9

一句话总结

本研究通过Orr机制，在准二维（Q2D）指数边界层中识别出一种亚临界湍流转捩，该过程仅由最优Tollmien–Schlichting（TS）波扰动驱动。非线性增长，特别是TS波的拱形变形及在流向速度片中的能量储存，使能量增益比线性机制高出数个数量级，且更长的计算域扩展了能触发持续湍流的初始能量范围。

ABSTRACT

The link to the online abstract of this manuscript, accepted in Phys. Rev. Fluids, is https://journals.aps.org/prfluids/accepted/32074S4aH8b1c608e19768b42571f9001086a3f44. A subcritical route to turbulence via purely quasi-two-dimensional mechanisms, for a quasi-two-dimensional system composed of an isolated exponential boundary layer, is numerically investigated. Exponential boundary layers are highly stable, and are expected to form on the walls of liquid metal coolant ducts within magnetic confinement fusion reactors. Subcritical transitions were detected only at weakly subcritical Reynolds numbers (at most $\\approx 70$% below critical). Furthermore, the likelihood of transition was very sensitive to both the perturbation structure and initial energy. Only the quasi-two-dimensional Tollmien-Schlichting wave disturbance, attained by either linear or nonlinear optimisation, was able to initiate the transition process, by means of the Orr mechanism. The lower initial energy bound sufficient to trigger transition was found to be independent of the domain length. However, longer domains were able to increase the upper energy bound, via the merging of repetitions of the Tollmien-Schlichting wave. This broadens the range of initial energies able to exhibit transitional behaviour. Although the eventual relaminarization of all turbulent states was observed, this was also greatly delayed in longer domains. The maximum nonlinear gains achieved were orders of magnitude larger than the maximum linear gains (with the same initial perturbations), regardless if the initial energy was above or below the lower energy bound. Nonlinearity provided a second stage of energy growth by an arching of the conventional Tollmien-Schlichting wave structure. A streamwise independent structure, able to efficiently store perturbation energy, also formed.

研究动机与目标

• 在磁约束聚变反应堆液态金属冷却剂通道相关系统中，建立一种纯粹的准二维（Q2D）亚临界湍流转捩路径。
• 研究初始扰动结构与能量在触发亚临界转捩中的作用，重点关注Orr机制与非线性动力学。
• 确定域长对转捩上下限能量阈值及湍流态持续时间的影响。
• 量化非线性增益相对于线性增益的大小，并评估Q2D MHD系统中能量储存与再激发的潜力。

提出的方法

• 采用SM82模型对孤立的指数边界层进行数值模拟，该模型在强磁场条件下近似描述准二维MHD流。
• 应用线性和非线性最优扰动理论，通过迭代优化识别出最具有能量的初始扰动。
• 利用边缘追踪与直接数值模拟探测吸引盆与转捩阈值。
• 通过能量范数分析瞬态增长，比较线性和非线性放大机制。
• 在更长域中研究涡旋合并与波的汇聚，以评估持续湍流及在流向速度片中的能量储存。
• 在超算集群（NCI、Pawsey、MonARCH）上采用周期性边界条件与高分辨率谱方法，确保数值精度。

实验结果

研究问题

• RQ1 能否在无三维不稳定性或随机噪声的情况下，实现纯粹的准二维亚临界湍流转捩？
• RQ2 Tollmien–Schlichting波及其非线性扭曲形成的“拱形”结构在Q2D边界层中实现亚临界转捩中起何作用？
• RQ3 域长与扰动能量如何影响湍流转捩的上下限阈值？
• RQ4 非线性机制在该系统中使能量增长超出线性瞬态放大的程度如何？
• RQ5 为何所有湍流态最终都会重新层流化？这是数值伪影还是Q2D湍流吸引子固有的不稳定性所致？

主要发现

• 仅在弱亚临界雷诺数（低于临界值约70%）下观察到亚临界湍流转捩，且仅当通过Orr机制由最优准二维Tollmien–Schlichting波激发时才发生。
• 转捩的初始能量下限阈值（$E_{\text{D}}$）与域长无关，但更长的域通过重复TS波结构的合并，显著提高了上限阈值（$E_{\text{D},2}$）。
• 非线性增益比线性增益高出数个数量级：在雷诺数约低于和高于临界值40%时，非线性增益分别达到约~4×10³和~2×10⁴，而线性增益分别为约~90和~166。
• 传统TS波结构的拱形变形使即使在低于下限能量阈值时也能实现显著的非线性增长，能量被储存在沿流向延伸的负速度片中，可调制基本流。
• 所有情况下湍流态最终均重新层流化，但在更长域中该过程显著延迟，表明存在更持久的瞬态湍流。
• 拱形TS波的形成及后续的能量储存表明，可能存在流动控制策略，即使从低能初始扰动出发，也能重新激发湍流。