Numerical modelling of wildland fire spread on the windward and leeward sides of a ridge.
Thomas, C.M., J. Sharples and J. Evans
In Weber, T., McPhee, M.J. and Anderssen, R.S. (eds) MODSIM2015, 21st International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2015, pp. 312-318. ISBN: 978-0-9872143-5-5., 2015.
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.
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Last updated 31st January 2013