Minimal seeds are the smallest amplitude perturbations that trigger transition to turbulence in a subcritical flow. They are presented in the Stokes boundary layer, the oscillating flow of a viscous fluid above a flat plate, at a fixed initial phase corresponding to the timing of the Stokes boundary layer's optimal linear transient growth, at two moderate Reynolds numbers, and in two domains accommodating one and two wavelengths of the linearly optimal growing mode. Although the minimal seed trajectories are dominated by the flow's large linear transient growth at early times, only 77% of the initial energy is formed from the linearly optimal growing mode; the remainder ensures that nonlinear interaction transfers energy from spanwise- to streamwise- independent structures, and makes up for a timing mismatch between the end of linear transient growth and the production phase of the edge state (the saddle point separating the laminar and turbulent basins of attraction).
Variational identification of minimal seeds to trigger transition in plane Couette flow
一个变分制剂纳入完整的纳维-斯托克斯方程被用来识别初始扰动与有限的动能E_{0}产生最大的增益扰动动能（在所有可能的时间间隔）平面Couette流。选择了两种不同的代表性流动几何形状，对应于Butler & Farrell（1992）和Monokrousos等人（2011）之前使用的几何形状。在前（较小的几何）的情况下，E_{0}从0增加，我们找到了一个最佳的，这是一个光滑的非线性延续的著名的线性结果在$E_{0} = 0$。然而，在$E_{0} = E_{c}$中，完全不相关的状态未被发现，这触发了湍流，因此我们的算法无法收敛。由于$E_{0} \rightarrow E^{+}_{c}, we find good evidence that the turbulence triggering initial conditions approach a 'minimal seed' which corresponds to the state of lowest energy on the laminar-turbulent basin boundary or 'edge'. This situation is repeated in the Monokrousos et al. (2011) (larger) geometry albeit with one notable n…
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Scuola Superiore Meridionale, School for Advanced Studies（南方高等研究院）；SISSA International School for Advanced Studies Mathematics Area, mathLab（国际高等研究学院数学领域）；Institute of Science Technology for Energy Sustainable Mobility (STEMS) Consiglio Nazionale delle Ricerche (CNR)（能源可持续交通科学与技术研究所（STEMS）意大利国家研究委员会（CNR））；Dipartimento di Matematica e Applicazioni “Renato Caccioppoli
