Transport between Two Fluids across Their Mutual Flow Interface: The Streakline Approach

Mixing between two different fluids with a mutual interface must be initiated by fluid transporting across this fluid interface, caused, for example, by applying an unsteady velocity agitation. In general, there is no necessity for this physical flow barrier between the fluids to be associated with extremal or exponential attraction, as might be revealed by applying Lagrangian coherent structures, finite-time Lyapunov exponents, or other methods on the fluid velocity. It is shown that streaklines are key to understanding the breaking of the interface under velocity agitations, and a theory for locating the relevant streaklines is presented. Simulations of streaklines in a cross-channel mixer and a perturbed Kirchhoff elliptic vortex are quantitatively compared to the theoretical results. Additionally, a methodology for quantifying the unsteady advective transport between the two fluids using streaklines is presented and verified numerically for the same two examples.