A Simple Model for Wildland Fire Vortex–Sink Interactions

A model is developed to explore fire–atmosphere interactions due to the convective sink and vorticity sources in a highly simplified and idealized form, in order to examine their effect on spread and the stability of various fire front geometries. The model is constructed in a cellular automata framework, is linear, and represents a background flow, convective sink, and vortices induced by the fire plume at every burning cell. We use standard techniques to solve the resulting Poisson equations with careful attention to the boundary conditions. A modified Bresenham algorithm is developed to represent convection. The three basic flow types—large-scale background flow, sink flow, and vortex circulation—interact in a complex fashion as the geometry of the fire evolves. Fire-generated vortex–sink interactions produce a range of fire behavior, including unsteady spread rate, lateral spreading, and dynamic fingering. In this simplified framework, pulsation is found associated with evolving fire-line width, a fire-front acceleration in junction fires, and the breakup of longer initial fire lines into multiple head fires. Fuel is very simply represented by a single burn time parameter. The model fuel is uniform yet patchiness occurs due to a dynamic interaction of diffusive and convective effects. The interplay of fire-induced wind and the geometry of the fire front depends also on the fuel burn time.