Lu presents findings on the hydrodynamic stability of a premixed flame subjected to transverse shear. The problem configuration is a situation of interest for laminar and turbulent flames when they travel into a region of shear.
The linear stability problem is first analytically solved, and the dispersion relation is determined. The effects of the transverse shear and thermal expansion are examined. Lu’s research then carried out a weakly nonlinear analysis in the weak thermal expansion limit and derived the modified Michelson-Sivashinsky (MS) equation, which describes the evolution of the flame surface. Numerical solutions of the MS equation show that due to the transverse shear, the flame develops a skewed cusp-like structure, that steadily propagates into the unburned gases and simultaneously translates along the transverse direction. The fully nonlinear evolution of premixed flames with a realistic density jump is then investigated using the Direct Numerical Simulation (DNS) approach.