A Similarity Technique for Solving Two-Layer Shallow-Water Equations

Magda M. Kassem, Medhat M. Helal, Mohammad L. Mekky, Emad A. Mohamed

Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt.

DOI: 10.4236/am.2012.34047                

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.

Keywords

The Characteristic Function Method; The Two-Layer Shallow-Water Equations; Gravity Currents

Conflicts of Interest

The authors declare no conflicts of interest.

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