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J. W. Rottman and R. E. Grundy, “Self-Similar Solutions of the Shallow-Water Equations Representing Gravity Currents with Variable Inflow,” Journal of Fluid Mechanics, Vol. 169, 1986, pp. 337-351. doi:10.1017/S0022112086000678

has been cited by the following article:

• 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.