Mathematical modelling of wildfire spread
Lead Research Organisation:
University College London
Department Name: Mathematics
Abstract
Research Areas:
Continuum mechanics
Fluid dynamics and aerodynamics
Recent 2019-2020 wildfires in California and Australia caused catastrophic environmental damage. In the summer of 2018, the UK experienced unusually large-scale wildfires most notably on Saddleworth Moor. Smoldering peatland megafires, the largest and longest burning fires on Earth, are responsible for the emission of 15% of global greenhouse gases.
The evolution of wildfire fronts is a complex process involving fluid dynamics, thermodynamics and consideration of terrain and vegetation types e.g. fire spread in eucalypt forests involves different processes than that of smoldering peat. At its simplest the spread of a combustion front is a problem of an evolving curve in two dimensions: a classic two-dimensional free boundary problem. Kinematic effects of advection by prevailing winds play an important role in this evolution, as well as geometric effects such as front curvature. Mathematical modelling incorporating physical and geometric effects will be used study the stability and spatial patterns formed by advancing combustion fronts. Techniques and methods employed in other areas of applied and pure mathematics such as free boundary problems, Hele-Shaw flows and mean-curvature flows, will be used to understand wildfire front evolution. Other important effects such a the merger of wildfire fronts will be considered.
Continuum mechanics
Fluid dynamics and aerodynamics
Recent 2019-2020 wildfires in California and Australia caused catastrophic environmental damage. In the summer of 2018, the UK experienced unusually large-scale wildfires most notably on Saddleworth Moor. Smoldering peatland megafires, the largest and longest burning fires on Earth, are responsible for the emission of 15% of global greenhouse gases.
The evolution of wildfire fronts is a complex process involving fluid dynamics, thermodynamics and consideration of terrain and vegetation types e.g. fire spread in eucalypt forests involves different processes than that of smoldering peat. At its simplest the spread of a combustion front is a problem of an evolving curve in two dimensions: a classic two-dimensional free boundary problem. Kinematic effects of advection by prevailing winds play an important role in this evolution, as well as geometric effects such as front curvature. Mathematical modelling incorporating physical and geometric effects will be used study the stability and spatial patterns formed by advancing combustion fronts. Techniques and methods employed in other areas of applied and pure mathematics such as free boundary problems, Hele-Shaw flows and mean-curvature flows, will be used to understand wildfire front evolution. Other important effects such a the merger of wildfire fronts will be considered.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509577/1 | 01/10/2016 | 24/03/2022 | |||
| 2417313 | Studentship | EP/N509577/1 | 11/01/2021 | 10/01/2025 | Samuel Harris |
| EP/T517793/1 | 01/10/2020 | 30/09/2025 | |||
| 2417313 | Studentship | EP/T517793/1 | 11/01/2021 | 10/01/2025 | Samuel Harris |
| Description | From our publication: a two-dimensional model for the evolution of the fire line - the interface between burned and unburned regions of a wildfire - is formulated. The fire line normal velocity has three contributions: (i) a constant rate of spread representing convection and radiation effects; (ii) a curvature term that smooths the fire line; and (iii) a Stefan-like term in the direction of the oxygen gradient. While the first two effects are geometrical, (iii) is dynamical and requires the solution of the steady advection-diffusion equation for oxygen, with advection owing to a self-induced 'fire wind', modelled by the gradient of a harmonic potential field. The conformal invariance of this coupled pair of partial differential equations, which has the Péclet number as its only parameter, is exploited to compute numerically the evolution of both radial and infinitely long periodic fire lines. A linear stability analysis shows that fire line instability is possible, dependent on the ratio of curvature to oxygen effects. Unstable fire lines develop finger-like protrusions into the unburned region; the geometry of these fingers is varied and depends on the relative magnitudes of (i)-(iii). It is argued that for radial fires, the fire wind strength scales with the fire's effective radius, meaning that increases in time, so all fire lines eventually become unstable. For periodic fire lines, remains constant, so fire line stability is possible. The results of this study provide a possible explanation for the formation of fire fingers observed in wildfires. |
| Exploitation Route | The numerical method used provides an alternative, computationally cheap, way to simulate wildfire spread. Our research is continuing to develop the model to incorporate other factors affecting wildfire spread, e.g. wind effects. |
| Sectors | Education,Environment,Other |