Evolution and breaking of liquid film flowing on a vertical cylinder

Philip Rosenau, Alexander Oron

Research output: Contribution to journalArticlepeer-review


An amplitude equation is derived, which describes the evolution of a disturbed film interface H(τ,Z,Y) flowing down an infinite vertical cylindrical column. Using a new approach, which accounts for fast spatial changes, the nonlinear evolution of the interface is shown to be governed by Hτ + βHHz + αHzz + γ∇2{N [ (1/ω2)H + ∇2H ]} = 0, where ω is the normalized cylinder radius and α, β, and γ are constants, ∇ ≡ (∂Z, ∂Y), and N= [ 1 + ∈4(∇H)2] -3/2. It is shown numerically that for some linearly unstable equilibria the evolving waves break in a finite time.

Original languageEnglish
Pages (from-to)1763-1766
Number of pages4
JournalPhysics of fluids. A, Fluid dynamics
Issue number11
StatePublished - 1989


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