Numerical modelling of wildland fire spread on the windward and leeward sides of a ridge.

The interaction of one fire with another can substantially alter the behaviour of the individual fires. This may occur, for example, during the coalescence of spot fires or when separate fire fronts merge. The resulting fire-fire interactions may lead to unexpected, and in some cases extreme, fire behaviour. One manifestation of this behaviour is a change in the rates of spread of the individual fires. Viegas et al. (2012) studied this effect analytically and experimentally in the case of the intersection of two line fires meeting at an acute angle, and have reported on the so-called ‘jump fire’ phenomenon whereby initially the fire front in the vicinity of the intersection of the two fires advances very rapidly. They interpreted this as a rotation of the lines of fire, however it may also be interpreted in terms of the curvature of the merged fire front. Indeed, Sharples et al. (2013) were able to qualitatively reproduce the ‘jump fire’ behaviour using a simple numerical model of frontal evolution in which the rate of spread in the normal direction is dependent on the curvature of the fire line. Such curvature dependent flows occur elsewhere in nature, for example in the growth of crystals and in gas-phase flame propagation, and have been studied extensively (Sethian, 1985). In the context of wildfire, possible mechanisms for such an effect include atmosphere-fire interactions and geometric effects relating to the radiative and convective transfer of energy. The inclusion of curvature dependence may be a tractable way to incorporate the effects of these complex phenomena into models of fire spread that do not currently accommodate them. To determine the extent to which this curvature effect is captured by a coupled atmosphere-fire model (WRF-Fire) we perform numerical experiments and analyse the relationship between the rate of spread and the curvature of the modelled front. This study focuses on geometric configurations of fires similar to those considered by Viegas et al. (2012). The coupled atmosphere-fire simulations produced patterns of fire propagation that were qualitatively similar to those reported by Viegas et al. (2012). This is despite a significant difference in the spatial scales of the two studies: the experiments of Viegas et al. (2012) considered fire lines a few metres in length, while those considered here are about one kilometre long. The main feature of the coupled simulations was the formation of a strong convective updraft between the two fire lines near their point of intersection, which caused that part of the merged fire to advance more rapidly. Comparisons with simulations in which the two fire lines were allowed to burn independently indicated that pyroconvective coupling between the two fire lines increased the overall rate of advance of the intersection point by a factor of about 7-10. As such, the simulations suggest that a fire spreading under similar scenarios will propagate with a considerable dynamic element. Local fire-line curvature was calculated and compared with instantaneous rates of spread to test the hypothesis that the rapid advance of the point of intersection can be thought of as a curvature effect. This comparative analysis did not find that large negative curvature is associated with higher rates of spread; in fact the highest rates of spread in the simulations were consistently associated with parts of the fire line with local curvature very close to zero. However, the analysis presented here does not rule out the existence of such a curvature effect in some mean sense.

Figure 3. Composite plot of fire-line evolution from three model runs made with WRF-Fire under the same conditions as Figure 1. The blue line illustrates the evolution of the front after only the northern arm is ignited, i.e. with no fire-fire interaction. The green line is the corresponding front for the southern arm. The red and white line, identical to that in Figure 1, shows the front when both arms are ignited simultaneously.