Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension

We consider the Rayleigh-Taylor instability in two finite-thickness fluids including the effects of viscosity and surface tension. The eight equations expressing boundary, continuity, and jump conditions imposed on the eigenfunction are written in the form MV=0 where M is an 8×{}8 matrix andV is a vector containing the eight coefficients that appear in the eigenfunction. Exact numerical results are obtained by solving det(M)=0, the dispersion relation which determines the growth rate {γ} as a function of the physical parameters of the system. For the case of a semi-infinite viscous fluid with a free surface the exact result is given analytically. We also derive an approximate analytic formula for arbitrary thicknesses, compare it with the exact results, and briefly discuss recent experiments on finite-thickness fluids. {} 1996 The American Physical Society.