Fully localised nonlinear energy growth optimals in pipe flow
Fully localised nonlinear energy growth optimals in pipe flow
复制标题
管流中完全局部化的非线性能量增长优化
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Kerswell
中科院分区：
文献类型：
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作者：
C. Pringle;A. Willis;R. Kerswell
在给定的质量流率下，在大时间和长管道域中发现了一个新的、完全局部化的能量增长优化。这个最优出现在一个阈值扰动能量之下，在这个阈值扰动能量之下，已知的（与流无关的）线性最优的非线性版本[P。J. Schmid和D. S. Henningson，“hageno - poiseuille流的最佳能量密度增长”，J.流体力学，277,192-225(1994)]被选中，并且在触发过渡的临界能量之前似乎保持最佳状态。这种最优的形式类似于在短管道中发现的[Pringle等人，“剪切流湍流的最小种子：使用非线性瞬态增长来接触混沌的边缘，”J.流体力学，702,415-443(2012)]，但现在在流向上完全定位。这种完全局部化的最优扰动代表了“真实”（实验室）管道流动的最小种子（任意接近能够触发湍流事件的状态的最小扰动）的最佳近似。计算了最优解对若干参数的依赖关系，证明了结构的鲁棒性。
A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shear flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust.