AN EVOLUTION EQUATION MODELING INVERSION OF TULIP FLAMES

We attempt to reduce the number of physical ingredients needed to mode l the phenomenon of tulip-flame inversion to a bare minimum. This is a chieved by synthesising the nonlinear, first-order Michelson-Sivashins ky (MS) equation with the second order linear dispersion relation of L andau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behaviour and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numeric al solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows th at the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.