Mathematical modeling of wildfire dynamics

Abstract

Wildfires continue to pose a long-standing threat in our society. In this thesis, I derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two-dimensional flow around a rising plume above a concentrated heat source modeling a fire line. This flow assumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. The flow outside the plume is described by a Biot-Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady evolution of the mass, momentum, energy, and vorticity inside the plume, with sources derived to model mixing in the style of Morton et al. (1956).

The fire in the above plume model is taken to be a stationary point source fire with properties calculated from the fire model. The effects of fire dynamics are modeled using a control volume derivation to write equations for total density, fuel density, oxygen density, and energy. This fire model allows the fire to propagate, where the plume and fire models are coupled through the point source fire and ambient air flow, allowing for a feedback mechanism between the two models. The derivation and implementation of the fire model are extended to investigate the situations of slope driven fires. The results show that the models presented in this thesis are capable of capturing the complex dynamics present in a wildfire. Specifically, the models address the complex interaction of the fire and fire plume with the surrounding air, fuel layer, and topography.