tangential velocity gradient across the interface, and can be thought of as a viscous counterpart of the Kelvin-
The time-dependent motion for a two-layer Couette flow consisting of fluids of different viscosities is simulated numerically by Helmholtz instability.
using an algorithm based on the Volume of Fluid (VOF) method.
A difficulty in the theory of flows involving more than Interfacial tension is included via a continuous surface force (CSF) one fluid lies in the nonuniqueness of solutions, and the algorithm. The algorithm is fine-tuned to handle the motion which question of which interface shapes would be observed.
is driven by a shear-induced interfacial instability due to the viscosity A first step toward the answer concerns the stability of stratification. The code is validated against linear theory. Two prototypical situations are presented, one at a moderately high Reynolds certain families of interfacial shapes that are observed number and the other at a lower Reynolds number. The initial condiin experiments. In two-layer Couette flow, the base tion is seeded with the eigenmode of largest growth rate, with velocity profile is linear in each fluid with a flat interface.
amplitudes that are varied from those that capture the linear regime Linear stability analysis of this family of solutions estabto larger values for nonlinear regimes. Issues of free surface adveclishes windows in parameter space where the solution tion and viscosity interpolation are discussed. The onset of nonlinearity occurs at the interface and is quadratic, followed by wave may be observed. At the onset of a finite wavenumber steepening. แฎ 1997 Academic Press instability, the weakly nonlinear analysis of [5] determines whether the time-periodic traveling wave solution would saturate nonlinearly. This analysis determines windows of parameters where, for sufficiently small amplitude larities between Surfer and our code and it would be 346