Let and be the wavenumber (measured in units of planar laminar flame thickness ) and the growth rate (measured in units of the residence time of the planar laminar flame) of the perturbations to the planar premixed flame. Then the Clavin–Garcia dispersion relation is given by[2][3][4][5][6]
where
and
Here
is the
gas expansion ratio; ratio of burnt gas to unburnt gas density; typically ;
is the ratio of density-
thermal conductivity product to its value in the unburnt gas;
is the ratio of temperature to its unburnt value, defined such that ;
^Searby, G., & Clavin, P. (1986). Weakly turbulent, wrinkled flames in premixed gases. Combustion science and technology, 46(3-6), 167-193.
^Truffaut, J. M., & Searby, G. (1999). Experimental study of the Darrieus-Landau instability on an inverted-‘V’flame, and measurement of the Markstein number. Combustion science and technology, 149(1-6), 35-52.
^Clavin, P., & Searby, G. (2016). Combustion waves and fronts in flows: flames, shocks, detonations, ablation fronts and explosion of stars. Cambridge University Press.
^Matalon, M. (2018). The Darrieus–Landau instability of premixed flames. Fluid Dynamics Research, 50(5), 051412.
^Al Sarraf, E., Almarcha, C., Quinard, J., Radisson, B., Denet, B., & Garcia-Ybarra, P. (2019). Darrieus–Landau instability and Markstein numbers of premixed flames in a Hele-Shaw cell. Proceedings of the Combustion Institute, 37(2), 1783-1789.