Effective geometric front dynamics for premixed turbulent combustion with separated velocity scales

We study the large scale effective flame front equations for premixed turbulent combustion with separated scale turbulent velocity fields recently formulated and derived by Majda and Souganidis. For the particular case of a steady incompressible velocity field consisting of a mean flow plus a small scale periodic shear we use analytical expressions and numerical quadrature to study the effective turbulent flame front velocity, its dependence on the turbulence intensity, and the role played by the mean flow. In general the dependence of the turbulent flame speed on the turbulence intensity is nonlinear, and the local logarithmic rate of growth can take a continuum of values, depending on the magnitudes of the mean and turbulent intensities. In the weak turbulence limit this dependence can be either linear or quadratic, depending on the magnitude and direction of the mean flow relative to the shear. In the strong turbulence limit the dependence is always linear. This behavior is documented for various forms of the small scale shear flow.