Publication Date:
1983-10-01
Description:
We study the existence and the role of solitary waves in the instability of a fluid layer flowing down an inclined plane. The approach presented is fully nonlinear. Solitary waves steady in a moving frame are described by homoclinic trajectories of an associated ordinary differential equation. They are searched numerically for a given value of viscosity and surface tension. Several kinds of solitary waves can exist, characterized by their number n of humps. We investigate the stability of these waves by integrating the initial value problem directly. Solitary waves with more than 1 hump did not appear in the simulation, and moreover a catastrophic behaviour took place for too large a Reynolds number (R ≳ R1) or too large an amplitude, suggesting a finite time singularity. The long term evolution is shown to be a very slow relaxation to a steady state in a moving frame. The relation to the experimental observation of localized wavetrains is also discussed. © 1983, Cambridge University Press. All rights reserved.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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