A Simple Model for Wildland Fire Vortex–Sink Interactions

Abstract

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.

Turbulent Wildland Fire Spread by Ember Wash

“…The model CA domain is defined by a two-dimensional rasterized grid and solved by decomposing the velocity into the sum of an irrotational and a solenoidal velocity field (Quaife and Speer, 2021). The first component is a background velocity that we take to be the uniform velocity UBG.…”

“…We use an idealized 2D model for near-surface wind in the presence of fire to investigate ember-enhanced spread in the presence of fire-atmosphere interaction (Quaife and Speer, 2021). The divergent flow is induced by the rising buoyant fire plume that entrains surrounding air, and the rotational flow at the surface is induced by the lifting of horizontal background vorticity by the buoyant plume.…”

Fingering instability in wildfire fronts

“…Irrespective of the assumptions made here, modelling the flow exterior to wildfires and plumes using solutions of the two-dimensional Laplace equation has been used previously by e.g. Weihs & Small (1986), Maynard, Princevac & Weise (2016), Sharples & Hilton (2020), Quaife & Speer (2021) and Kaye & Linden (2004). Further, it is assumed that the fire wind velocity u is much larger than the normal velocity v n of the fire line, so the system is quasi-steady.…”

“…2018), the wind can also be treated as irrotational, so satisfies the Laplace equation Irrespective of the assumptions made here, modelling the flow exterior to wildfires and plumes using solutions of the two-dimensional Laplace equation has been used previously by e.g. Weihs & Small (1986), Maynard, Princevac & Weise (2016), Sharples & Hilton (2020), Quaife & Speer (2021) and Kaye & Linden (2004).…”

“…Although not mentioned explicitly, the Dold et al (2005) assumption that the burn rate, or fire line speed, is proportional to the oncoming airflow feeding the fire appears analogous to the oxygen effect considered in this paper. Recently, Quaife & Speer (2021) used a two-dimensional, reduced physics, cellular automata model of fire-atmosphere interaction incorporating a fire-plume-induced convective sink, and vorticity sources at the flanks of the fire. Amongst a variety of fire line behaviours observed in their model was fingering, in the form of the breakup of the fire line into multiple advancing heads.…”