Author(s)

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.

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.

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

M. Kassem, M. Helal, M. Mekky and E. Mohamed, "A Similarity Technique for Solving Two-Layer Shallow-Water Equations," Applied Mathematics, Vol. 3 No. 4, 2012, pp. 315-321. doi: 10.4236/am.2012.34047.