Intense vortices have been observed within large-scale bushfires, and have been likened to “fire tornadoes”. This paper presents a simple mathematical model of such an event, and is based on a Boussinesq approximation relating temperature and density in the air. A linearized model is derived under the assumption that the temperature varies only slightly from ambient, and a solution to that model is presented in closed form. The nonlinear equations are solved in axisymmetric geometry, using a semi-numerical approach based on Fourier–Bessel series. The nonlinear and linearized results are in good agreement for small temperature excursions above ambient, but when larger deviations occur, nonlinear effects cause a type of flow reversion within the fire vortex. The cause of this effect is discussed in the paper.
