Role of flow topology in wind-driven wildfire propagation

The paper derives, via scaling, a neutral curve in the (Da, Φ) plane and reports a robust power-law fit Φ ≈ m Da^n with n ≈ 0.8564; it also demonstrates manifold-guided front advance/stalling in a steady saddle flow and FTLE-based predictions, resonance, and phase inversion in a double-gyre. The candidate model provides a compatible, slightly more mechanistic front-normal reduction yielding an explicit algebraic neutral relation A/Φ = B/Da + R (hence Φ(Da) = A Da/(R Da + B)), explains why an apparent power law with 0 < n < 1 emerges over finite Da-windows, rigorously identifies unstable/stable manifold roles in the saddle, and gives a small-parameter averaging argument (O(λ/St)) and a continuity argument for phase inversion. Minor mismatches are mostly of presentation: the paper’s ‘invariance’ of the exponent is asserted empirically rather than proved, and the model’s diffusion-scale B omits the K′(T)(∇T)^2 contribution explicitly (though it can be absorbed into B). Overall, the conclusions agree and the proofs differ.