Fourier–physical space coherent structure in flame–vortex interactions relevant to flame–turbulence interactions using a new signal periodization procedure

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.