The dynamics of a spreading wildfire is modeled by using a variant of the Small World Network stochastic model (Zekri et al., 2005). The temporal evolution of the fire front width and its pattern’s fractal dimension exhibits an anomalous relaxation process before the extinction of the initial fire-line that is well described by a Kohlrausch–Williams–Watts-like relaxation function. The decrease of the fire pattern’s dimension corresponds to a transition from a structured fire front induced by the collective effects of burning fuels to a dispersed one caused by their individual effects. This anomalous relaxation with an exponent $\gamma \approx 0.5$ indicates the existence of a sub-diffusion process of the spreading fire regardless of the impact length and fuel occupation density. After the extinction of the initial fire-line, the fractal dimension of the fire pattern fluctuates around an average value corresponding to an average spread rate of fire and front intensity. The amplitude of these fluctuations decreases as the impact length of the burning fuel or the occupation density increases. The analysis of the local scale exponents shows that the fractal (self-similar) behavior of the fire pattern is observed in the spatial resolution range delimited by the mean free path and the pattern size. Further discussion on the competition effect between the heat release rate of the flame and the mean free path on fire behavior is provided.

通过使用小世界网络随机模型的变体（Zekri 等，2005）对野火蔓延的动态进行建模。火锋宽度的时间演变及其模式的分形维数在初始火线消失之前表现出异常的松弛过程，这可以通过类似 Kohlrausch-Williams-Watts 的松弛函数很好地描述。火灾模式维度的减少对应于从由燃烧燃料的集体效应引起的结构化火锋过渡到由它们各自的影响引起的分散的火锋。这种具有指数的异常松弛$\gamma \approx 0.5$表明无论撞击长度和燃料占有密度如何，都存在蔓延的火势的子扩散过程。初始火线熄灭后，火型的分形维数在平均火势蔓延率和锋强对应的平均值附近波动。这些波动的幅度随着燃烧燃料的撞击长度或占据密度的增加而减小。局部尺度指数的分析表明，在由平均自由程和图案尺寸界定的空间分辨率范围内观察到火图案的分形（自相似）行为。进一步讨论了火焰的热释放率和平均自由程对火灾行为的竞争效应。