Accession Number : AD0715958

Title :   Asymptotic Nonlinear Wave Motion of a Viscous Fluid in an Inclined Channel of Arbitrary Cross Section.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Shen,M. C. ; Shih,S. M.

Report Date : FEB 1970

Pagination or Media Count : 33

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)

Descriptors :   (*FLUID FLOW, EQUATIONS OF MOTION), (*PARTIAL DIFFERENTIAL EQUATIONS, PERTURBATION THEORY), REYNOLDS NUMBER, NAVIER STOKES EQUATIONS, BOUNDARY VALUE PROBLEMS, INTEGRALS, NUMERICAL INTEGRATION, TWO DIMENSIONAL FLOW

Subject Categories : Numerical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE