标题： 分离流过NACA0012翼型的全局求解分析 显示英文标题

标题： Biglobal resolvent analysis of separated flow over a NACA0012 airfoil

摘要： 雷诺数在$Re=1000$、$2500$、$5000$和$10000$上对攻角为$\alpha=14^\circ$的二维 NACA0012 翼型分离流的影响通过大全局求解分析进行研究。 我们在频率、展向波数和折扣参数的范围内识别模态结构和能量放大，提供了不同时间尺度的见解。 使用时间折扣，我们发现剪切层动力学在短时间范围内占主导地位，而尾涡动力学在长时间范围内成为主要的放大机制。 展向效应在长时间范围内也出现，由低频维持。 在固定时间尺度下，我们研究雷诺数对响应和激励模态结构以及不同频率上的能量增益的影响。 在所有雷诺数下，响应模态从低频下的尾涡主导结构转变为高频下的剪切层主导结构。 主导机制发生变化的频率与雷诺数无关。 响应模态结构在不同雷诺数下显示出相似性，局部顺流波长仅取决于频率。 在不同攻角（$\alpha=9^\circ$）下的比较显示，随着频率增加，从尾涡到剪切层动力学的转变只有在非定常流是三维的情况下才会发生。 我们还研究了不同攻角和雷诺数下与尾涡和剪切层动力学相关的主导频率，并为每种机制展示了特征标度。 显示英文摘要

摘要： The effects of Reynolds number across $Re=1000$, $2500$, $5000$, and $10000$ on separated flow over a two-dimensional NACA0012 airfoil at an angle of attack of $\alpha=14^\circ$ are investigated through the biglobal resolvent analysis. We identify modal structures and energy amplifications over a range of frequency, spanwise wavenumber, and discount parameter, providing insights across various timescales. Using temporal discounting, we find that the shear layer dynamics dominates over short time horizons, while the wake dynamics becomes the primary amplification mechanism over long time horizons. Spanwise effects also appear over long time horizon, sustained by low frequencies. At a fixed timescale, we investigate the influence of Reynolds number on response and forcing mode structures, as well as the energy gain over different frequencies. Across all Reynolds numbers, the response modes shift from wake-dominated structures at low frequencies to shear layer-dominated structures at higher frequencies. The frequency at which the dominant mechanism changes is independent of the Reynolds number. The response mode structures show similarities across different Reynolds numbers, with local streamwise wavelengths only depending on frequency. Comparisons at a different angle of attack ($\alpha=9^\circ$) show that the transition from wake to shear layer dynamics with increasing frequency only occurs if the unsteady flow is three-dimensional. We also study the dominant frequencies associated with wake and shear layer dynamics across the angles of attack and Reynolds numbers, and present the characteristic scaling for each mechanism.