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Wildfires propagate through interactions between wind, fuel, and terrain, resulting in complex behaviors that challenge accurate predictions. This study investigates the interaction between wind velocity topology and wildfire dynamics, aiming to enhance our understanding of wildfire spread patterns through a simplified nonlinear convection–diffusion–reaction wildfire model, adopting a fundamental reactive flow dynamics perspective. We revisited the non-dimensionalizion of the governing combustion model by incorporating three distinct time scales. This approach revealed two new non-dimensional numbers, contrasting with the conventional non-dimensionalization that considers only a single time scale. Through scaling analysis, we analytically identified the critical determinants of transient wildfire behavior and established a state-neutral curve, indicating where initial wildfires extinguish for specific combinations of the identified non-dimensional numbers. Subsequently, a wildfire transport solver was developed, integrating upwind compact schemes and implicit–explicit Runge–Kutta methods. We explored the influence of stable and unstable manifolds in wind topology on the transport of wildfire under steady wind conditions defined using a saddle-type fixed point flow, emphasizing the role of the non-dimensional numbers. Additionally, we considered the benchmark unsteady double-gyre flow, examined the effect of unsteady wind topology on wildfire propagation, and quantified the wildfire response to varying wind oscillation frequencies and amplitudes using a transfer function approach. The results were compared to Lagrangian coherent structures (LCS) used to characterize the correspondence of manifolds with wildfire propagation. The approach of utilizing the wind flow manifolds provides valuable insight into wildfire dynamics across diverse wind scenarios, offering a potential tool for improved predictive modeling and management strategies.