论文标题
在二维通道流中局部波数据包的衰减和生长期间的图案保存
Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow
论文作者
论文摘要
在本文中，从数值和理论上研究了二维平面poiseuille流中局部波数据包（LWP）的衰减和生长。当雷诺数（$ re $）小于关键值$ re_c $时，扰动动能$ e_k $ e_k $ e_k $随着时间和经历的三个衰减期，即初始和最终的陡峭下降时期和中高原时期。衰减的LWP的较高初始$ e_k $对应于更长的寿命。根据模拟，生命周期为$（re_c-re）^{ - 1/2} $，表明生命周期的分歧为$ re $ $ $ the $ re_c $，这是一种称为“关键减速下降”的现象。 By proposing a pattern preservation approximation, i.e. the integral kinematic properties (e.g. the disturbance enstrophy) of an evolving LWP are independent of $Re$ and single valued functions of $E_k$, the disturbance kinetic energy equation can be transformed into the classical differential equation for saddle-node bifurcation, by which the lifetimes of decaying LWPs can be derived, supporting the $ -1/2 $缩放法。此外，通过应用图案保存近似值以及以$ re <re_c $获得的积分运动属性，雷诺数的数字和整个下部分支的相应$ e_k $，转弯点，上行lwps us $ e_k <0.15 $的上行能量范围是扰乱的能量，指示了一个扰乱的能量。 结构。
In this paper, the decay and growth of localized wave packet (LWP) in two-dimensional plane-Poiseuille flow are studied numerically and theoretically. When the Reynolds number ($Re$) is less than a critical value $Re_c$, the disturbance kinetic energy $E_k$ of LWP decreases monotonically with time and experiences three decay periods, i.e. the initial and the final steep descent periods, and the middle plateau period. Higher initial $E_k$ of a decaying LWP corresponds to longer lifetime. According to the simulations, the lifetime scales as $(Re_c-Re)^{-1/2}$, indicating a divergence of lifetime as $Re$ approaches $Re_c$, a phenomenon known as "critical slowing-down". By proposing a pattern preservation approximation, i.e. the integral kinematic properties (e.g. the disturbance enstrophy) of an evolving LWP are independent of $Re$ and single valued functions of $E_k$, the disturbance kinetic energy equation can be transformed into the classical differential equation for saddle-node bifurcation, by which the lifetimes of decaying LWPs can be derived, supporting the $-1/2$ scaling law. Furthermore, by applying the pattern preservation approximation and the integral kinematic properties obtained as $Re<Re_c$, the Reynolds number and the corresponding $E_k$ of the whole lower branch, the turning point, and the upper-branch LWPs with $E_k<0.15$ are predicted successfully with the disturbance kinetic energy equation, indicating that the pattern preservation is an intrinsic feature of this localized transitional structure.
