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+ε4(∇H)2]−3/2. It is shown numerically that for some linearly unstable equilibria the evolving waves break in a finite time.
No takes yet. Share an insight, caveat, or question.
Rosenau et al. (1989) studied this question.