论文标题
kolmogorov强迫的平行平行流的分叉
Bifurcations of a plane parallel flow with Kolmogorov forcing
论文作者
论文摘要
我们研究二维kolmogorov在通道中的主要分叉的，而被选为模拟平行流的边界条件，即分别在流向和跨度方向上的周期性和自由滑移边界条件。控制参数是基于摩擦系数的雷诺数，称为$ RH $。我们发现，随着我们增加$ rh $，层流稳定流通过退化的HopF分叉，振荡频率和增长模式的幅度在阈值处为零。还原的四模型模型捕获了从数值模拟获得的量表。随着我们增加$ RH $，我们观察到了二次不稳定性，它激发了该域中最大的模式。发现最大模式的饱和振幅被发现缩放为$ 3/2 $ $ 3/2 $的距离，距离阈值也可以使用低维模型来解释。
We study the primary bifurcations of a two-dimensional Kolmogorov flow in a channel subject to boundary conditions chosen to mimic a parallel flow, i.e. periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. The control parameter is the Reynolds number based on the friction coefficient, denoted as $Rh$. We find that as we increase $Rh$ the laminar steady flow goes through a degenerate Hopf bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. A reduced four-mode model captures the scalings that are obtained from the numerical simulations. As we increase $Rh$ further we observe a secondary instability which excites the largest mode in the domain. The saturated amplitude of the largest mode is found to scale as a $3/2$ power-law of the distance to the threshold which is also explained using a low-dimensional model.
