论文标题
基于平均流线性分析的模棱两可
Ambiguity in mean-flow-based linear analysis
论文作者
论文摘要
关于湍流平均值的Navier-Stokes方程的线性化构成了流行的能量扩增模型和相干结构，包括分析分析。虽然可以使用许多不同的因变量集等于编写Navier-Stokes方程，但我们表明，通过线性化获得的线性操作员的属性涉及平均值取决于在线性化之前写入方程的变量。例如，我们表明，使用原始和保守的变量会导致湍流射流分解算子的奇异值和模式的差异，并且随着可变密度效应的增加，差异变得更加严重。缺乏基于均值的线性分析的独特性为通过特定的变量选择提供了新的机会来优化模型，同时还强调了对非线性术语进行仔细考虑的重要性，而非线性术语则是对分辨率运算符的强迫。
Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimizing models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator.
