The nonlinear behavior of a sheared immiscible fluid interface

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Abstract
The two-dimensional Kelvin–Helmholtz instability of a sheared fluid interface separating immiscible fluids is studied by numerical simulations. The evolution is determined by the density ratio of the fluids, the Reynolds number in each fluid, and the Weber number. Unlike the Kelvin–Helmholtz instability of miscible fluids, where the sheared interface evolves into well-defined concentrated vortices if the Reynolds number is high enough, the presence of surface tension leads to the generation of fingers of interpenetrating fluids. In the limit of a small density ratio the evolution is symmetric, but for a finite density difference the large amplitude stage consists of narrow fingers of the denser fluid penetrating into the lighter fluid. The initial growth rate is well predicted by inviscid theory when the Reynolds numbers are sufficiently high, but the large amplitude behavior is strongly affected by viscosity and the mode that eventually leads to fingers is longer than the inviscidly most unstable one.