Turbulence Spectra and Cospectra Measured during Fire Front Passage
Daisuke Seto, Craig B. Clements, and Fred SnivelyDaisuke Seto, Craig B. Clements, and Fred SnivelyDepartment of Meteorology and Climate ScienceDepartment of Meteorology and Climate Science
San José State UniversitySan José State UniversitySan José, CASan José, CA
Warren E. Heilman Warren E. Heilman Northern Research StationNorthern Research Station
USDA Forest Service USDA Forest Service East Lansing, MIEast Lansing, MI
San José State UniversityFire Weather Research Laboratory
Overview of Presentation
• Background
• Experimental datasets
• Data processing
• Results– Velocity and temperature spectra– Momentum and heat flux cospectra
• Preliminary Conclusion
• Future WorkSan José State University
Fire Weather Research Laboratory
Background and Motivation
• Fire-atmosphere coupling occurs over spatial scales from tens of meters to kilometers.
→spectral analysis of in-situ turbulence data allows for the general description of turbulence structure over frequency domain.
• Fire spread rate predictions would be improved by accounting for the effect of turbulence (Albini 1983; Sun et al. 2009).
• Spectral analysis is used for – parameterizing eddy diffusivities – estimating dispersion coefficients
• Validity of surface layer similarity theory must be questioned when used for wildland fire applications.
San José State UniversityFire Weather Research Laboratory
Experimental Datasets
San José State UniversityFire Weather Research Laboratory
Grass fire in valley (CA)-head fire
Grass fire on slope (CA)-head fire
Sub-canopy burn (NC)-backing fire
slash burn (Finland)-backing fire
10:30 11:00 11:30 12:00 12:30 13:00 13:30 14:00 14:3020
30
40
50
60
70
80
90
100
110
Ts
Data Processing• Wind velocity and temperature (10Hz): ATI Sx-probe
– U: mean wind direction– V: lateral wind direction– W: tilt corrected vertical velocity– Ts: sonic temperature
• Define Pre-, During-, Post-Fire Front Passage (FFP)• Spectra and cospectra were calculated every 30 min,
using Fast Fourier Transform (FFT) algorithm before smoothing and averaging.
San José State UniversityFire Weather Research Laboratory 0.001 0.01 0.1 1 10
0.001
0.01
0.1
1
10
f = frequency
fS(f
)
rawsmoothed
Post-FFP
During-FFP
Pre-FFP
Tem
pera
ture
(°C
)
Result: Grass Fire in Valley
San José State UniversityFire Weather Research Laboratory
z = 6.7 m
Upre = 2.27 m/s
UFFP = 3.33 m/s
Upost = 3.67 m/s
Grass fire in valley (CA)
Spectra: Grass Fire in ValleyU
V
W
Ts
f = frequency
f S
(f)
-2/3
Grass Fire on Slope
San José State UniversityFire Weather Research Laboratory
z = 11 m
Upre = 6.23 m/s
UFFP = 7.03 m/s
Upost = No data
Grass fire on slope (CA)
Spectra: Grass Fire on Slopef
S(f
)U W
V Ts
f = frequency
-2/3
Sub-canopy
San José State UniversityFire Weather Research Laboratory
z = 3 m
Upre = 1.04 m/s
UFFP = 1.77 m/s
Upost = 1.08 m/s
Sub-canopy (NC)
Spectra: Sub-canopyf
S(f
)U W
V Ts
f = frequency
-2/3
Spectra: Sub-Canopy
Slash Burn
San José State UniversityFire Weather Research Laboratory
z = 11 m
Upre = 1.43 m/s
UFFP = 2.76 m/s
Upost = No data
slash burn (Finland)
Spectra: Slash Burnf
S(f
)U W
V Ts
f = frequency
-2/3
Normalized Spectral Density: Pre- and Post-FFP
n = fz/U
f S
(f)/
T*2
U W
V Ts
Stability class
f S
(f)/
u *2
Normalized Spectral Density: During-FFPf
S(f
)/u *2
n = fz/U
U W
V Ts
f S
(f)/
T*2
Stability class
Normalized momentum and heat flux cospectra-f
Cuw
(f)/
u *2
-f C
wT(f
)/u *
T*
n = fz/U
Momentum flux
Heat flux
Pre- and Post-FFP
Pre- and Post-FFP
During-FFP
During-FFP
Summary
• Unique velocity and temperature spectra were observed in each burn during FFP.
• Increases in velocity spectra may be related to the degree of coupling between fire and atmosphere.
• Increased temperature spectra was observed over entire frequency range in all cases.
• Surface layer similarity theory is valid for Pre- and Post-FFP velocity and temperature spectra.
• Normalized velocity spectra during FFP did not collapse into one curve. However, overall slope was conserved at higher frequencies.
• One universal behavior observed during FFP in all cases was a slower roll-off at both low and high frequencies in the normalized spectral curves.
• This is due to increased spectral density at all frequencies.
• Ambient turbulence is strongly affected by the fire front
San José State UniversityFire Weather Research Laboratory
Future Work
• Find empirical formula for velocity, temperature, and turbulence dissipation rate during FFP.
• Compare Ts spectral characteristics with measured total and radiative heat flux spectra.
San José State UniversityFire Weather Research Laboratory
Acknowledgements
• Dr. Tara Strand
• Grant # JFSP
• This research is also supported by Joint Venture Research Agreement from the USDA Northern Research Station #07-JV-11242300-073.
San José State UniversityFire Weather Research Laboratory