A NUMERICAL STUDY OF PERIODIC DISTURBANCES ON 2-LAYER COUETTE FLAW

The flow of two viscous liquids is investigated numerically with a vol ume of fluid scheme. The scheme incorporates a semi-implicit Stokes so lver to enable computations at low Reynolds numbers, and a second-orde r velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theo ry for a Hopf bifurcation. Examples of long-time wave saturation are s hown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimension s as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity diffe rence. Results at low Reynolds numbers show elongated fingers in two d imensions that break in three dimensions to form drops, while differen t topological changes take place at higher Reynolds numbers. (C) 1998 American Institute of Physics. [S1070-6631(98)00612-6].