Nonlinear evolution and breaking of interfacial Rayleigh-Taylor waves

Alexander Oron, Philip Rosenau

Research output: Contribution to journalArticlepeer-review

Abstract

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, γ = ∈A(τ,ξ),∈≪1, is shown to be governed by the regularized Kuramoto-Sivashinsky equation A τ + βAAξ + {αA + γA ξξ/(1 + ∈4Aξ2) 3/2}ξξ = 0, where the constants α,β, and γ are determined at equilibrium, ξ is the slow coordinate along the channel, ξ = ∈(x - c0t), and τ = ∈2t. It is shown numerically that for ∈2≥0.1β linearly unstable waves (while always of finite amplitude) are propelled by convection toward breaking in a finite time.

Original languageEnglish
Pages (from-to)1155-1165
Number of pages11
JournalPhysics of fluids. A, Fluid dynamics
Volume1
Issue number7
DOIs
StatePublished - 1989
Externally publishedYes

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