Numerical Study of the Unified Kadomtsev-Petviashvili Equation.
Abstract
In this paper, we numerically investigate the unified Kadomtsev-Petviashvili (uKP) equation derived by Chen & Liu (1995), which described weakly nonlinear and dispersive surface and interfacial waves propagating primarily in the longitudinal direction of a slowly rotating channel with varying topography on the propagation of a solitary wave in a stationary channel and a Kelvin solitary wave in a rotating channel. We find that in the absence of rotation, an oblique incident solitary wave propagating over a three-dimensional shelf in a straight wide channel will eventually develop into a series of uniform straight-crested solitary waves, together with a train of small oscillatory waves propagating upstream; with proper phase shifts, the shapes of these final two-dimensional solitary waves coincide with the shapes of those final solitary waves emerged from a corresponding normal incident solitary wave propagating over a corresponding two-dimensional shelf. In a two-layered rotating channel, the variation of topography does not have much effect on the propagation of a Kelvin solitary wave of depression, whereas it can have a significant influence on the propagation of a Kelvin solitary wave of elevation. Explanations for these numerical findings are given. (AN)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1995
- Accession Number
- ADA296029
Entities
People
- Philip L. Liu
- Yongze Chen
Organizations
- University of Delaware