Large-Eddy Simulation (LES) is a powerful formulation for model turbulent reacting flows that balances lower resolution with predictions of variance dominant momentum and energy fluctuations. Central to the LES framework is the need to model nonlinear interactions between the variance-dominant resolved-scale (RS) motions and subfilter-scale (SFS) fluctuations. A central feature of premixed turbulent combustion is nonlinear flame-turbulence interactions, a key element that involves advective nonlinear coupling between velocity and momentum, energy and species concentration. In this work, we extract the dominant RS-SFS advective nonlinear interactions to isolate SFS content that underlies the evolution of the resolved scales for encap-sulation within mathematical forms for potential use in advanced modeling strategies. We take advantage of the mathematical simplicity of the Fourier spectral description of the equations of motion where advective nonlinearities are given by a sum of “triadic” interactions each of which involves three Fourier modes whose wave-vectors form a triangle in multidimensional Fourier space. This elemental representation of key nonlinearities is used to develop a novel strategy to arrange and down-select the dominant nonlinear RS-SFS couplings underlying the evolution of RS motions, and extract the corresponding SFS content associated with dynamically dominant RS-SFS dynamics. The procedure is applied to analysis of “reduced physics” simulations of flame-vortex interactions with a new method for analysis of non-periodic signals in multi-dimensional Fourier-space. For primary variables with dominant variane in the grid-resolved scales and fast decay of energy into the subfilter scales, the resolved-scale features of the dynamically dominant SFS content are shown to be coupled with the smaller resolved scales characterizing the corrugations and thickness of the RS flame front. In contrast, the dynamically dominant SFS content of intermediate species involved in heat release extend farther in Fourier space to smaller scales. These SFS fluctuations are shown to follow the smallest flame-front corrugations, which deviate from the RS flame geometry in regions with high curvature, such as the flame cusps. The results of this study provide insights relevant to advanced modeling strategies designed to capture key RS-SFS couplings into prediction of RS dynamics.