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 optimization, 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 behavior. 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.

中文翻译：

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在准二维边界层中通过Orr机理产生亚临界湍流

对由孤立的指数边界层组成的准二维系统，通过纯准二维机制产生的亚临界湍流路径进行了数值研究。指数边界层是高度稳定的，预计会在磁约束聚变反应堆内的液态金属冷却剂管道壁上形成。仅在弱亚临界雷诺数下检测到亚临界转变（最多$\approx 70$低于严重百分比）。此外，过渡的可能性对扰动结构和初始能量都非常敏感。只有通过线性或非线性优化获得的准二维Tollmien-Schlichting波扰动，才能通过Orr机制来启动过渡过程。发现足以触发跃迁的较低初始能量束缚与畴长度无关。但是，更长的区域通过合并托尔米恩-施利希特波的重复，能够增加能量上限。这扩大了能够表现出过渡行为的初始能量的范围。尽管最终观察到了所有湍流状态的重新分层，但在更长的域中这也大大延迟了。无论初始能量是高于还是低于能量下限，获得的最大非线性增益都比最大线性增益大几个数量级（具有相同的初始扰动）。非线性通过传统的Tollmien-Schlichting波结构的拱形提供了能量增长的第二阶段。还形成了能够有效地存储扰动能量的沿流方向独立的结构。