Role of flow topology in wind-driven wildfire propagation

TL;DR

This work investigates how wind-flow topology governs wind-driven wildfire propagation within a physics-based nonlinear convection–diffusion–reaction framework. By introducing three characteristic time scales, the authors identify two key nondimensional numbers, $Da$ and $\Φ$, and derive a neutral-curve criterion that marks when fire heating balances cooling. They develop a GPU-accelerated solver using upwind compact schemes, IMEX-RK time stepping, and localized artificial diffusion, and couple this with Lagrangian coherent structures to relate steady saddle and unsteady double-gyre wind topologies to firefront dynamics. The study reveals that steady-flow manifolds strongly influence front paths and stalling under convection-dominated regimes, while unsteady wind induces resonance-like asymmetric advection when wind oscillations align with the fuel-reaction timescale; instantaneous FTLE fields can outperform time-averaged fields in such cases. While grounded in a simplified CDR-fire formulation, the results highlight how flow topology can inform risk assessment and guiding firefighter strategies, and point to future work integrating more detailed chemistry and fully coupled CFD–wildfire models with realistic terrain and firebrands.

Abstract

Wildfires propagate through intricate interactions between wind, fuel, and terrain, resulting in complex behaviors that pose challenges for accurate predictions. This study investigates the interaction between wind velocity topology and wildfire spread dynamics, aiming to enhance our understanding of wildfire spread patterns. We revisited the non-dimensionalizion of the governing combustion model by incorporating three distinct time scales. This approach revealed two new non-dimensional numbers, contrasting with the conventional non-dimensionalization that considers only a single time scale. Through scaling analysis, we analytically identified the critical determinants of transient wildfire behavior and established a state-neutral curve, indicating where initial wildfires extinguish for specific combinations of the identified non-dimensional numbers. Subsequently, a wildfire transport solver was developed using a finite difference method, integrating compact schemes and implicit-explicit Runge-Kutta methods. We explored the influence of stable and unstable manifolds in wind velocity on wildfire transport under steady wind conditions defined using a saddle-type fixed point flow, emphasizing the role of the non-dimensional numbers. Additionally, we considered the benchmark unsteady double-gyre flow and examined the effect of unsteady wind topology on wildfire propagation, and quantified the wildfire response to varying wind oscillation frequencies and amplitudes using a transfer function approach. The results were compared to Lagrangian coherent structures (LCS) used to characterize the correspondence of manifolds with wildfire propagation. The comprehensive approach of utilizing the manifolds computed from wind topology provides valuable insights into wildfire dynamics across diverse wind scenarios, offering a potential tool for improved predictive modeling and management strategies.

Figures (10)

• Figure 1: Temporal evolution of the initialized firefront temperature under the influence of various parameters. (a) A zero-valued contour of $\partial \overline{T}/\partial \tau$ is highlighted, representing the neutral curve along with the heating ($\partial \overline{T}/\partial \tau > 0$) and cooling ($\partial \overline{T}/\partial \tau < 0$) zones over the Da--$\Phi$ non-dimensional plane. (b) Inverse activation energy $\epsilon$, (c) inverse non-dimensional conductivity coefficient $\overline{\kappa}$, and (d) non-dimensional phase change temperature $\overline{T}{\text{pc}}$ are shown in the same plane. The dotted arrows indicate the incremented directions of these dimensionless parameters.
• Figure 2: The two wind patterns considered in this study. (a) Steady wind topology showcasing both stable (blue) and unstable (red) manifolds, with a saddle point positioned at the origin, superimposed with velocity streamlines. (b) Unsteady double gyre wind velocity at $\tau = 0$, where the dividing streamline (blue) shows the boundary between the two vortices. The vertical dividing streamline undergoes translation motion along the $\xi$ axis, oscillating about the value of $1$, with a given amplitude and frequency over time.
• Figure 3: Spatio-temporal evolution of the Heaviside firefront under a saddle-type steady wind velocity field over a uniformly distributed fuel bed, computed across a range of Da values $\in (1, 10, 10^2, 10^3, 10^4, 10^5)$, with $\Phi = 1.0$ and $\epsilon = 0.03$. (a) Fuel and temperature fields at various time instants are displayed in the top and bottom rows, respectively, for $Da = 10^3$, with streamlines superimposed at $\tau = 0.01$. At $\tau = 0.15$, the firefront locations are marked by white strips, labeled as the top firefront ($F_T^{Y}$), bottom firefront ($F_B^{Y}$), right firefront ($F_R^{X}$), and left firefront ($F_L^{X}$), with superscripts indicating their movement direction. (b) The instantaneous spatial advection of the firefronts and their corresponding time-averaged group velocities are shown, depicted in the top and bottom rows, respectively. The dotted horizontal line represents the asymptotically converged group velocity of the firefronts at an infinite $Da$ number.
• Figure 4: Spatio-temporal evolution of the Heaviside firefront under a saddle-type steady wind velocity field over a uniformly distributed fuel bed, computed across a range of $\Phi$ values $\in (100, 10, 1, 0.1, 0.05, 0.01)$, with $Da = 10^3$ and $\epsilon = 0.03$. (a) Fuel and temperature fields at various time instants, with the top and bottom rows, respectively, computed for $\Phi = 0.05$. Streamlines are superimposed at $\tau = 0.1$ and $\tau = 0.6$. At $\tau = 0.60$, the dotted white curve highlights the local neutral curve, indicating the stalled top and bottom firefronts over the fuel bed. (b) Instantaneous spatial advection of the firefronts and their corresponding time-averaged group velocities, depicted in the top and bottom rows, respectively. The red dots highlight the group velocity of stalled firefronts along their respective advecting directions.
• Figure 5: Spatio-temporal evolution of the Heaviside firefront under a saddle-type steady wind velocity field over a uniformly distributed fuel bed, computed across varying $\epsilon$ values $(0.35, 0.40, 0.45)$, with $Da = 10^3$ and $\Phi = 0.05$. (a) Fuel and temperature fields at different time instants, with the top and bottom rows corresponding to each field, respectively, calculated for $\epsilon = 0.035$. Streamlines are superimposed at $\tau = 0.05$ over the fuel bed. (b) Instantaneous spatial advection of the four firefronts is plotted. (c) Instantaneous fuel burning rate over time is plotted.