Quasi-Stationary Wave Evolution on a Falling Film
We examine the quasi-stationary approximation of nonlinear two-dimensional wave evolution on a falling film with numerical experiments and analyses. It is found that, unless the noise spectrum contains an inordinate amount of nearly neutral ω/ω 0 > 0.9 and nearly static ω/ω 0 < 0.05 frequencies, the waves behave in a quasi-stationary manner at every location downstream from the feed. Secondary wave evolution can hence be modeled as successive and increasingly long near misses of weakly unstable stationary waves via their stable and unstable manifolds. Wave selection and the entire evolution downstream can then be accurately predicted with simple models.
KeywordsFalling film coherent structures solitary waves homoclinic and heteroclinic orbits subharmonic resonance
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