Nonlinear evolution and breaking of interfacial Rayleigh–Taylor waves

The nonlinear evolution of interfacial waves separating liquids of different viscosity and density (Rayleigh–Taylor instability) in a 2-D channel is studied. Using a new approach, which accounts for large gradients, the nonlinear evolution of the interface, y=εA(τ,ξ),ε≪1, is shown to be governed by the regularized Kuramoto–Sivashinsky equation Aτ +βAAξ+{αA+γAξξ/ (1+ε4A2ξ)3/2}ξξ=0, where the constants α,β, and γ are determined at equilibrium, ξ is the slow coordinate along the channel, ξ=ε(x−c0t), and τ=ε2t. It is shown numerically that for ε2≥0.1β linearly unstable waves (while always of finite amplitude) are propelled by convection toward breaking in a finite time.