论文标题
壁构成湍流的降级模型中的结构相互作用
Structure interactions in a reduced-order model for wall-bounded turbulence
论文作者
论文摘要
新的还原阶模型（ROM）是针对正弦剪切流（也称为Waleffe流）和小型周期域中的平面轴向流的。 Waleffe流的第一个派生利用了傅立叶模式，这形成了该问题的天然正顺序基础。通过Navier-Stokes方程的Galerkin投影获得了此基础的ROM。大型基础减少到12个模式，这些模式在维持混乱的湍流动力学方面显着贡献。与较早的ROM的关键区别是包含两个滚动式结构，其跨度波长等于$ l_z $和$ l_z/2 $，其中$ l_z $是计算框的跨度长度。通过重写相同的12个模式的Galerkin系统，将所得系统适应了Couette流，并经过修改以满足墙壁上的无滑动条件。由此产生的动态系统导致有限的寿命与较早的rom和小域中的模拟一致。但是，目前的模型显示的寿命比早期的ROM长得多，差异远远超过一个数量级。将COUETTE-FLOW模型与直接数值模拟（DNS）的结果进行比较，统计数据显示公平一致。 $ l_z $和$ l_z/2 $ lengthscales的包含是较长的湍流寿命的关键功能：忽略任何滚动模式或其非线性互动，会导致湍流寿命的急剧降低。因此，当前的ROM突出了一些与长期湍流相关的主要非线性相互作用。
New reduced-order models (ROMs) are derived for sinusoidal shear flow (also known as Waleffe flow) and plane Couette flow in small periodic domains. A first derivation for Waleffe flow exploits Fourier modes that form a natural orthonormal basis for the problem. A ROM for such basis is obtained by a Galerkin projection of the Navier-Stokes equation. A large basis was reduced to 12 modes that contribute significantly in maintaining chaotic, turbulent dynamics. A key difference from earlier ROMs is the inclusion of two roll-streak structures, with spanwise wavelengths equal to $L_z$ and $L_z/2$, where $L_z$ is the spanwise length of the computational box. The resulting system was adapted to Couette flow by rewriting the Galerkin system for the same 12 modes, modified so as to satisfy no-slip conditions on the walls. The resulting dynamical systems lead to turbulence with finite lifetimes, in agreement with earlier ROMs and simulations in small domains. However, the present models display lifetimes that are much longer than in earlier ROMs, with differences of more than an order of magnitude. The Couette-flow model is compared to results of direct numerical simulation (DNS), with statistics displaying fair agreement. The inclusion of the $L_z$ and $L_z/2$ lengthscales is seen to be a key feature for longer turbulence lifetimes: neglecting any of the roll modes, or their non-linear interaction, leads to drastic reductions of turbulence lifetimes. The present ROMs thus highlight some of the dominant nonlinear interactions that are relevant in maintaining turbulence for long lifetimes.
