Performing global resolvent analysis for high-Reynolds-number turbulent flow calls for the handling of a large discrete operator. Even though such a large operator is required in the analysis, most applications of resolvent analysis extracts only a few dominant resolvent response and forcing modes. Here we consider the use of randomized numerical linear algebra to reduce the dimension of the resolvent operator for achieving computational speed up and memory saving compared to the standard resolvent analysis. To accomplish this goal, we utilize sketching of the linear operator with random test matrices with a Gaussian distribution and with insights from the base flow incorporated to perform singular value decomposition on a low-rank matrix holding dominant characteristics of the full resolvent operator. The strength of the randomized resolvent analysis is demonstrated on a turbulent separated flow over an airfoil. This randomized approach clears the path towards tackling resolvent analysis for higher-Reynolds-number bi- and triglobal base flows.

中文翻译：

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随机分解剂分析

对高雷诺数湍流进行全局分解剂分析需要处理大型离散算子。尽管分析中需要这么大的运算符，但是大多数解析物分析应用程序仅提取少数主导的解析物响应和强制模式。在这里，我们考虑使用随机数值线性代数来减少分解算子的维数，与标准的分解剂分析相比，可实现计算速度的提高和内存的节省。为实现此目标，我们利用具有高斯分布的随机测试矩阵以及结合基本流的见解，利用线性算子的草图，对包含完整可分辨算子的主导特征的低秩矩阵执行奇异值分解。机翼上湍流分离的流动证明了随机溶解物分析的强度。这种随机方法为解决更高雷诺数双向和三全局基流的分解物分析扫清了道路。