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 new feature - the appearance of a nonlinear optimal (as found recently in pipe flow by Pringle & Kerswell (2010) and boundary layer flow by Cherubini et al. (2010)) at finite $ E_{0} < E_{c} $ which has a very different structure to the linear optimal. Again the minimal seed at $ E_{0} = E_{c} $不类似于线性或非线性最优。我们的研究结果支持Pringle等人（2011）最近提出的两个假设中的第一个，但与第二个相矛盾。重要的是，他们的预测，即优化的泛函形式对于识别E_{c}并不重要，只要湍流产生的值增加：我们发现看起来是相同的E_{c}和最小的种子使用能量增益，而不是Monokrousos等人（2011）几何中的总耗散。
英文摘要：
A variational formulation incorporating the full Navier-Stokes equations is used to identify initial perturbations with finite kinetic energy E_{0} which generate the largest gain in perturbation kinetic energy (across all possible time intervals) for plane Couette flow. Two different representative flow geometries are chosen corresponding to those used previously by Butler & Farrell (1992) and Monokrousos et al. (2011). In the former (smaller geometry) case as E_{0} increases from 0, we find an optimal which is a smooth nonlinear continuation of the well-known linear result at $E_{0} = 0$. At $E_{0} = E_{c}$, however, completely unrelated states are uncovered which trigger turbulence and our algorithm consequently fails to converge. As $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 new feature - the appearance of a nonlinear optimal (as found recently in pipe flow by Pringle & Kerswell (2010) and boundary layer flow by Cherubini et al. (2010)) at finite $E_{0} < E_{c}$ which has a very different structure to the linear optimal. Again the minimal seed at $E_{0} = E_{c}$ does not resemble the linear or now the nonlinear optimal. Our results support the first of two conjectures recently posed by Pringle et al. (2011) but contradict the second. Importantly, their prediction that the form of the functional optimised is not important for identifying E_{c} providing heightened values are produced by turbulent flows is confirmed: we find the what looks to be the same E_{c} and minimal seed using energy gain as opposed to total dissipation in the Monokrousos et al. (2011) geometry.
