Propagation rate of growing interfaces in stirred fluids

Abstract

The overall propagation rate of growing interfaces subject to weak random stirring is investigated, based on a variant of the Kardar-Parisi-Zhang equation. Scaling analysis, supported by computations, indicates that random stirring increases the overall propagation rate in proportion to 4/3 power of the ratio of stirring rate to growth rate. The generally assumed quadratic dependence on this ratio is valid only for special cases such as periodic flow. On this basis, a modified turbulent-flame speed formula is proposed. Implications concerning interpretation of measurements are noted.