The aim of the current study is to characterize key multidimensional relationships between coherent structures in physical vs Fourier/scale space representations of flame–turbulence interactions, as a basis for future analysis of the nonlinear couplings between key resolved scale (RS) and subfilter scale (SFS) motions in large-eddy simulation (LES) of premixed turbulent combustion. However, applying the bounded Fourier transform (FTF) in the nonperiodic flame-normal direction requires the removal of nonphysical Fourier content from the boundary discontinuities. To this end, we have developed a broadly applicable “discontinuity pollution removal” procedure for application to the FTF of multidimensional signals with a single nonperiodic direction. The procedure balances periodization of the signal near the boundaries with minimization of signal modification away from the boundaries. We applied the procedure in a physical–Fourier space analysis of the interactions between a flame and single-scale eddies modeled as the impact of a train of two-dimensional (2D) vortices on an initially planar premixed flame. We find that a specific spectrally broad localized coherent structure in Fourier space connects RS to SFS fluctuations in thermal energy and species concentration that, in physical space, are localized to the corrugations in the flame front in response to eddy–flame interactions. Within the RS fluctuations of energy and species concentration, the flame corrugation structure in physical space is found to be localized to sub-volumes within the RS region of 2D Fourier space. This new understanding of physical–Fourier space relationships categorizes classes of RS–SFS interactions relevant to SFS modeling in LES of premixed turbulent combustion.

中文翻译：

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使用新信号周期化程序的与火焰-湍流相互作用有关的火焰-涡旋相互作用中的傅里叶-物理空间相干结构

当前研究的目的是表征火焰湍流相互作用的物理与傅立叶/尺度空间表示中的相干结构之间的关键多维关系，作为将来分析关键分辨尺度（RS）和子滤波器尺度之间的非线性耦合的基础（预混湍流燃烧的大涡模拟（LES）中的运动。但是，在非周期性火焰法线方向上应用有界傅立叶变换（FTF）需要从边界不连续中移除非物理傅立叶含量。为此，我们开发了一种广泛适用的“间断污染去除”程序，可将其应用于具有单个非周期性方向的多维信号的FTF。该过程平衡了边界附近的信号的周期化与远离边界的信号修改的最小化。我们将该程序应用于火焰与单尺度涡流之间相互作用的物理傅立叶空间分析中，该涡流建模为一列二维（2D）涡流对最初平面的预混火焰的影响。我们发现，傅立叶空间中一个特定的光谱宽广的局部相干结构将RS与SFS的热能和物质浓度波动相关联，在物理空间中，它们响应于涡流-火焰相互作用而局限在火焰前沿的波纹中。在能量和物质浓度的RS波动范围内，物理空间中的火焰波纹结构被发现局限于二维傅立叶空间RS区域内的子体积。