Model experiments and theory of flame front propagation in forest fire

To quantify how inter-source spacing (“spatial step”), inclination angle (slope), and wind affect flame-propagation velocity, model experiments were conducted in the present work. Propagation velocities and flame morphologies were quantified and visualized. The measured dependence of velocity on wind speed, slope, and source spacing is then used to formulate and illustrate a theory for forest-fire flame-front propagation affected by wind over flat and hilly terrains. The results demonstrate dramatic effect of wind on flame propagation and the overall configuration of the flame front, as well as a significant difference between highly volatile and flammable versus less flammable fuels. The model with continuous flame front developed in the present work approximates the cases where the tree-to-tree distances and the characteristic flame transfer times between trees are much smaller and shorter, respectively, than the sizes and evolution times of forest fire. The model implies that the flame propagation is sustained by volatiles rapidly released by plants in fire, which sustain fire propagation serving as a fuel mixing in a thin flame front with oxidizer from the ambient air like in diffusion flames. It is also implied that the flame front can be considered as continuous on its scale which is much larger than the tree-to-tree distances (that means the so-called diffusion approximation in the mathematical sense). The theoretical predictions reveal that the flame front configuration is strongly affected by landscape topography and wind, much more than by the initial ignition configuration. It should be emphasized that (i) the model lab-scale experiments here only elucidate on the physical level the main effects which are to be expected from the large-scale experiments: that flame propagation velocity strongly depends on fuel volatility, spacing between sources, terrain inclination, and wind presence. (ii) The large-scale predictive capability of the quasi-physical theoretical/numerical model developed here is still to be verified by fitting the two lumped parameters of the model to large-scale data. The latter is currently hardly possible because the available published data on distillation stage of forest fires are scarce and typically lacking many important details in their totality, like slopes and wind speed, the type of wood involved, the volatile and water content in the wood, etc. (iii) Accordingly, the present numerical results, albeit some of them were obtained for a real kilometer-scale landscape, are illustrative in nature. Still, in future widening of a detailed experimental data bank and its interpretation by such methods as Machine Learning and AI will allow a reliable and detailed verification of the present quasi-physical theoretical/numerical approach. That will yield potentially impactful insights into occurrence of forest fires around urban areas as well as of urban fires, with the present quasi-physical model being used for monitoring, advanced planning and mitigation.