Fingering instability in wildfire fronts. (25th July 2022)
- Record Type:
- Journal Article
- Title:
- Fingering instability in wildfire fronts. (25th July 2022)
- Main Title:
- Fingering instability in wildfire fronts
- Authors:
- Harris, S.J.
McDonald, N.R. - Abstract:
- Abstract: Abstract : 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 $\textit {Pe}$ 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 $\textit {Pe}$ increases in time, so all fire lines eventually become unstable. For periodic fire lines, $\textit {Pe}$ remains constant, so fire line stability isAbstract: Abstract : 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 $\textit {Pe}$ 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 $\textit {Pe}$ increases in time, so all fire lines eventually become unstable. For periodic fire lines, $\textit {Pe}$ 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. … (more)
- Is Part Of:
- Journal of fluid mechanics. Volume 943(2022)
- Journal:
- Journal of fluid mechanics
- Issue:
- Volume 943(2022)
- Issue Display:
- Volume 943, Issue 2022 (2022)
- Year:
- 2022
- Volume:
- 943
- Issue:
- 2022
- Issue Sort Value:
- 2022-0943-2022-0000
- Page Start:
- Page End:
- Publication Date:
- 2022-07-25
- Subjects:
- fingering instability -- combustion
Fluid mechanics -- Periodicals
532.005 - Journal URLs:
- http://www.journals.cambridge.org/jid%5FFLM ↗
http://firstsearch.oclc.org ↗ - DOI:
- 10.1017/jfm.2022.452 ↗
- Languages:
- English
- ISSNs:
- 0022-1120
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 22063.xml