标题： 剪切流的截断一维模型中的湍流转变 显示英文标题

标题： Turbulent transition in a truncated one-dimensional model for shear flow

摘要： 我们提出了一种用于剪切流中湍流转捩的简化模型，该模型足够简单以允许彻底的数值研究，同时允许比之前模态截断更复杂的时空动力学。 我们的模型允许比较在展向局部化的初始扰动与正弦扰动所产生的动力学之间的差异。 对于展向局部化的初始条件，亚临界转捩到“湍流”状态（i）发生得更加突然，层流与“湍流”流之间的边界似乎要不那么“结构化”， （ii）导致一个时空混沌的区域，在该区域内，时空复杂瞬态的寿命更长，并且对初始条件更加敏感。 使展向局部化初始扰动激发混沌瞬态所需的最小初始能量$E_0$随雷诺数$E_0 \sim Re^p$呈幂律变化，其中$p \approx -4.3$。 指数$p$仅弱依赖于局部化扰动的宽度，并且低于以往低维模型中通常观察到的值，通常为$p \approx -2$。 在固定雷诺数下，混沌瞬态的寿命分布被发现与指数分布一致。 显示英文摘要

摘要： We present a reduced model for the transition to turbulence in shear flow that is simple enough to admit a thorough numerical investigation while allowing spatio-temporal dynamics that are substantially more complex than those allowed in previous modal truncations. Our model allows a comparison of the dynamics resulting from initial perturbations that are localised in the spanwise direction with those resulting from sinusoidal perturbations. For spanwise-localised initial conditions the subcritical transition to a `turbulent' state (i) takes place more abruptly, with a boundary between laminar and `turbulent' flow that is appears to be much less `structured' and (ii) results in a spatiotemporally chaotic regime within which the lifetimes of spatiotemporally complicated transients are longer, and are even more sensitive to initial conditions. The minimum initial energy $E_0$ required for a spanwise-localised initial perturbation to excite a chaotic transient has a power-law scaling with Reynolds number $E_0 \sim Re^p$ with $p \approx -4.3$. The exponent $p$ depends only weakly on the width of the localised perturbation and is lower than that commonly observed in previous low-dimensional models where typically $p \approx -2$. The distributions of lifetimes of chaotic transients at fixed Reynolds number are found to be consistent with exponential distributions.