Fingering instability in wildfire fronts

A two-dimensional model for the evolution of fire line – interface between burned and unburned regions a wildfire is formulated. The normal velocity has three contributions: (i) constant rate spread representing convection radiation effects; (ii) curvature term that smooths line; (iii) Stefan-like in direction oxygen gradient. While first two effects are geometrical, dynamical requires solution steady advection–diffusion equation oxygen, with advection owing to self-induced ‘fire wind’, modelled by gradient harmonic potential field. conformal invariance this coupled pair partial differential equations, which Péclet number $\textit {Pe}$ as its only parameter, exploited compute numerically both radial infinitely long periodic lines. linear stability analysis shows instability possible, dependent on ratio effects. Unstable lines develop finger-like protrusions into region; geometry these fingers varied depends relative magnitudes (i)–(iii). It argued fires, wind strength scales fire's effective radius, meaning increases time, so all eventually become unstable. For lines, remains constant, possible. results study provide possible explanation formation observed wildfires.