Asymptotic Nonlinear Wave Motion of a Viscous Fluid in an Inclined Channel of Arbitrary Cross Section.
Abstract
A tractable asymptotic theory is achieved for the study of three-dimensional nonlinear wave motion of an incompressible, viscous fluid with surface tension in an inclined channel of arbitrary cross section. The method developed here is based upon a multiple-parameter singular perturbation scheme within the framework of long-wave approximation. The nonlinear problem is reduced to a sequence of linear elliptic mixed boundary-value problems, which can be solved by means of standard methods. These solutions are then used to determine the wave speed and evolution equations governing the nonlinear wave motion. The results obtained give a quantitative description of a three-dimensional bore structure in an inclined channel of arbitrary cross section, and critical Reynolds number is also defined as a criterion for the instability of the wave motion. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1970
- Accession Number
- AD0715958
Entities
People
- Meichang Shen
- S. M. Shih
Organizations
- University of Wisconsin–Madison