论文标题
从薄板到艾哈迈德的身体：矩形棱镜的线性和弱的非线性稳定性
From thin plates to Ahmed bodies: linear and weakly non-linear stability of rectangular prisms
论文作者
论文摘要
我们研究了层流的稳定性，过去的三维矩形棱镜。宽度与高度的比率设置为$ W/h = 1.2 $，而长度与高度比率$ 1/6 <l/h <3 $涵盖了从薄板到细长的艾哈迈德身体的广泛几何形状。首先，全球线性稳定性分析产生了一系列的干草叉和霍普夫分叉：（i）在下部雷诺数$ re $ $ re $，两种固定模式，$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a和$ b $，变得不稳定，分别打破顶/底/底/左/右平面对称性； （ii）在较大的$ re $上，两种振荡模式变得不稳定，并且每种模式都会打破两个对称性之一。这四种模式中的关键$ $随着$ l/h $的增加而增加，从质量上再现了轴对称唤醒中固定和振荡分叉的趋势（例如薄盘，球体和子弹形尸体）。接下来，基于两个固定模式$ a $ a $ a $ a $ a $ a $ a $ a $ a耦合振幅方程的弱非线性分析。对于艾哈迈德的身体，$ re $ $增加了状态$（a，0）$首先出现，其次是状态$（0，b）$。尽管这两个状态有一系列的双重性，但只有$（0，b）$在较大$ re $的情况下保持稳定，类似于在动荡政权中观察到的静态唤醒偏转（跨越较大的基本维度）。分叉序列（包括双重性和滞后）通过完全非线性的直接数值模拟进行了验证，并且证明对$ w $中的变化和$ l $在普通艾哈迈德体内的变化是可靠的。
We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$, while the length-to-height ratio $1/6<L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$, two stationary modes, $A$ and $B$, become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$, two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ of these four modes increase with $L/H$, qualitatively reproducing the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly non-linear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases state $(A,0)$ appears first, followed by state $(0,B)$. While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$, similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully non-linear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies.
