TITLE:
A Similarity Technique for Solving Two-Layer Shallow-Water Equations
AUTHORS:
Magda M. Kassem, Medhat M. Helal, Mohammad L. Mekky, Emad A. Mohamed
KEYWORDS:
The Characteristic Function Method; The Two-Layer Shallow-Water Equations; Gravity Currents
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.4,
April
27,
2012
ABSTRACT: This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.