论文标题
在粘弹管流中的大weissenberg-number缩放法律上
On the large-Weissenberg-number scaling laws in viscoelastic pipe flows
论文作者
论文摘要
这项工作解释了在Wan等人最近报道的大型Weissenberg-number（$ WI $）的轴对称性粘弹性管流的弱非线性分析中，衍生的Ginzburg-Landau方程（GLE）的第一个Landau系数的缩放定律。 J.流体机械。 （2021），第1卷。 929，A16。使用渐近方法，我们得出了一个还原的系统，该系统捕获了在危险条件附近的线性中心模式不稳定性的特性，该系统在较大的限制中。然后，基于减少的系统，我们使用多尺度扩展方法进行了弱非线性分析，该方法很容易解释了Landau系数的上述规模定律和其他一些扩展定律。特别是，在线性临界条件附近的干扰平衡幅度被发现缩放为$ Wi^{ - 1/2} $，这可能是实验者感兴趣的。当前的分析减少了参数和未知数的数量，并例证了一种研究大型$ Wi $的粘弹性流量的方法，这可能会使人们对其非线性动力学的理解有了新的启示。
This work explains a scaling law of the first Landau coefficient of the derived Ginzburg-Landau equation (GLE) in the weakly nonlinear analysis of axisymmetric viscoelastic pipe flows in the large-Weissenberg-number ($Wi$) limit, recently reported in Wan et al. J. Fluid Mech. (2021), vol. 929, A16. Using an asymptotic method, we derive a reduced system, which captures the characteristics of the linear centre-mode instability near the critical condition in the large-$Wi$ limit. Based on the reduced system we then conduct a weakly nonlinear analysis using a multiple-scale expansion method, which readily explains the aforementioned scaling law of the Landau coefficient and some other scaling laws. Particularly, the equilibrium amplitude of disturbance near linear critical conditions is found to scale as $Wi^{-1/2}$, which may be of interest to experimentalists. The current analysis reduces the numbers of parameters and unknowns and exemplifies an approach to studying the viscoelastic flow at large $Wi$, which could shed new light on the understanding of its nonlinear dynamics.
