Field equation for interface propagation in an unsteady homogeneous flow field

Abstract

The nonlinear scalar field equation governing the propagation of an unsteadily convected interface is used to derive a convenient expression for the average volume flux through such an interface in a homogeneous flow field. For a particular choice of the initial scalar field, the average volume flux through any such interface is expressed as a volume-averaged functional of the evolving scalar field, facilitating analysis based on renormalized perturbation theory and numerical simulation. It is noted that this process belongs to a different universality class from the propagation model of M. Kardar, G. Parisi, and Y.-C. Zhang [Phys. Rev. Lett. 56, 889 (1986)].