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The merging of two lines of fire is a relatively common occurrence in landscape fire events. For example, it can arise through the coalescence of two wildfires or when a prescribed fire meets a wildfire as part of suppression efforts. When two fires approach one another, the effects of convective and radiative heat transfer are compounded and high rates of spread can arise as a result. This is particularly the case when two lines of fire meet at some oblique angle the point of intersection on the newly merged fire can advance rapidly. This case was investigated recently by Viegas et al. (2012), who devised an analytical model to emulate the effects of energy concentration between the two merging fire lines. In this paper, we present a more geometric approach by considering the evolution of the merged fire as the flow of a plane curve with a normal speed that depends on the curvature of the fire front. Parametric variation of the curvature dependence is investigated, and the resultant geometric evolutions of the fire front are compared with the experimental observations of Viegas et al. (2012). Further theoretical aspects of plane curvature flows and their more general application to fire front modelling are also discussed. Junction fires occur when two fire lines meet at an oblique angle. The interaction of the two fire lines means that junction fires can exhibit unexpected fire behaviour, with enhanced rates of spread in the vicinity of the junction point. Junction fires also comprise one of the main fire behaviours involved in spot fire coalescence. Quantifying the interaction between two oblique fire lines is essential for the development of next generation fire spread models, which will allow for prediction of dynamic fire propagation. Previous work considered using fire line curvature as a simple means for modelling the dynamic behaviour of junction fires. However, in this preliminary work the method for modelling the fire spread was based on initial conditions that were not truly representative of merging fire lines. Subsequent work has implemented the curvature based model using a level set method, which allows for more natural boundary conditions. This approach was used to successfully simulate the behaviour of large-scale experimental grassland fires. In this paper we consider the same approach applied to experimental fires that are an order of magnitude smaller than those considered previously. Optimal parameters for the curvature based model applied to the smaller scale fires are derived and compared to the optimal parameters obtained for the larger scale fires. This comparison reveals information about how the dynamic behaviour of junction fires varies across different scales.

Modelling the dynamic behaviour of small scale junction fires using curvature flows