论文标题
频道流量和达西法的演变超出了关键雷诺数
Evolution of channel flow and Darcy law beyond the critical Reynolds number
论文作者
论文摘要
通道流程通常由Darcy Law和Poiseuille流量轮廓描述。但是，对于不可压缩的通道流，有一个临界状态，其特征是临界雷诺数$ re_c $和一个关键的波动向量MC，在此之后，在线性方向上，通道流变得不稳定。通过获得线性，不可压缩的，三维的（3D）Navier-Stokes（ns）方程的分析本函数，即流体动力学模式（HMS），我们将完整的NS方程降低到通过扩展的velocity in velocity的构成自动差异方程（ODES）系统的整个NS方程，以实现velocity;时间成为唯一的自变量。 NS方程的非线性项被转换为第三张张量，该张量伴侣对膨胀系数对成对以影响第三个时间变化。在线性制度中，与ORSZAG结果相比，$ re_c $的值可获得五个重要的数字精度。我们在数值上使用有限的热激发初始HMS以$ re> re_c $进化了自动频率，以找到净流速降低的波动平衡状态，并伴有涡流。从力量平衡的角度来看，在$ re> re_c $的柜台概况中发现了有趣的功能。
Channel flow is usually described by Darcy law with the Poiseuille flow profile. However, for incompressible channel flow there is a critical state, characterized by a critical Reynolds number $Re_c$ and a critical wavevector mc, beyond which the channel flow becomes unstable in the linear regime. By obtaining the analytical eigenfunctions of the linearized, incompressible, three dimensional (3D) Navier-Stokes (NS) equation in the channel geometry, i.e., the hydrodynamic modes (HMs), we reduce the full NS equation to a system of coupled autonomous ordinary differential equations (ODEs) by expanding the velocity in terms of the HMs; time becomes the only independent variable. The nonlinear term of the NS equation is converted to a third-rank tensor that couples pairs of the expansion coefficients to effect the time variation on the third. In the linear regime, the value of $Re_c$ is obtained to five significant digit accuracy when compared to the Orszag result. We numerically time evolve the autonomous ODEs at $Re>Re_c$ with a finite set of thermally excited initial HMs to find a fluctuating equilibrium state with a reduced net flow rate, accompanied by vortices. Through the perspective of force balance, interesting features are uncovered in the counter-flow profiles at $Re>Re_c$.
