Energy dissipation caused by boundary layer instability at vanishing viscosity
Energy dissipation caused by boundary layer instability at vanishing viscosity
复制标题
粘度消失时边界层不稳定性引起的能量耗散
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
K. Schneider
中科院分区：
文献类型：
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作者：
Natacha Nguyen van yen;Matthias Waidmann;R. Klein;M. Farge;K. Schneider
根据最近的数学和数值计算结果，提出了一个定性的解释的缩放能量耗散的高雷诺数流体流动与固体障碍物接触。渐近分析表明，它是由一个快速的，小规模的瑞利-托尔米恩-施利希廷不稳定性与不稳定的范围，其下限和上限的规模为$Re^{3/8}$和$Re^{1/2}$，分别。通过线性叠加，不稳定模态诱导了Re^{1}$级的边界涡量通量，根据Kato定理，这是分离和阻力产生的关键因素。这些预测证实了数值求解Navier-Stokes方程在一个二维的周期性通道离散使用紧凑的有限差分在壁法线方向，和一个频谱方案在壁平行方向。
A qualitative explanation for the scaling of energy dissipation by high-Reynolds-number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it is governed by a fast, small-scale Rayleigh–Tollmien–Schlichting instability with an unstable range whose lower and upper bounds scale as $Re^{3/8}$ and $Re^{1/2}$ , respectively. By linear superposition, the unstable modes induce a boundary vorticity flux of order $Re^{1}$ , a key ingredient in detachment and drag generation according to a theorem of Kato. These predictions are confirmed by numerically solving the Navier–Stokes equations in a two-dimensional periodic channel discretized using compact finite differences in the wall-normal direction, and a spectral scheme in the wall-parallel direction.