Turbulence Spectra and Cospectra Measured during Fire Front Passage Daisuke Seto, Craig B. Clements, and Fred Snively Department of Meteorology and Climate Science San José State University San José, CA Warren E. Heilman Northern Research Station USDA Forest Service East Lansing, MI San José State University Fire Weather Research Laboratory

Overview of Presentation Background Experimental datasets Data processing Results –Velocity and temperature spectra –Momentum and heat flux cospectra Preliminary Conclusion Future Work San 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 University Fire Weather Research Laboratory

Experimental Datasets San José State University Fire 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

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 University Fire Weather Research Laboratory Post-FFP During-FFP Pre-FFP Temperature (°C)

Result: Grass Fire in Valley San José State University Fire Weather Research Laboratory z = 6.7 m U pre = 2.27 m/s U FFP = 3.33 m/s U post = 3.67 m/s Grass fire in valley (CA)

Spectra: Grass Fire in Valley U V W Ts f = frequency f S(f) -2/3

Grass Fire on Slope San José State University Fire Weather Research Laboratory z = 11 m U pre = 6.23 m/s U FFP = 7.03 m/s U post = No data Grass fire on slope (CA)

Spectra: Grass Fire on Slope f S(f) UW VTs f = frequency -2/3

Sub-canopy San José State University Fire Weather Research Laboratory z = 3 m U pre = 1.04 m/s U FFP = 1.77 m/s U post = 1.08 m/s Sub-canopy (NC)

Spectra: Sub-canopy f S(f) UW VTs f = frequency -2/3 Spectra: Sub-Canopy

Slash Burn San José State University Fire Weather Research Laboratory z = 11 m U pre = 1.43 m/s U FFP = 2.76 m/s U post = No data slash burn (Finland)

Spectra: Slash Burn f S(f) UW VTs f = frequency -2/3

Normalized Spectral Density: Pre- and Post-FFP n = fz/U f S(f)/T * 2 UW VTs Stability class f S(f)/u * 2

Normalized Spectral Density: During-FFP f S(f)/u * 2 n = fz/U UW VTs f S(f)/T * 2 Stability class

Normalized momentum and heat flux cospectra -f C uw (f)/u * 2 -f C wT (f)/u * T * n = fz/U Momentum flux Heat flux Pre- and Post-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 University Fire 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 University Fire 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 San José State University Fire Weather Research Laboratory