SOME CONSIDERATIONS ON APPROXIMATE SOLUTION OF A DAM BREAK FLOW WITH BOTTOM SHEAR STRESSES

Abstract

 This paper proposes the derivation method of an approximate solution of shallow water equations for dam break flows, applying a perturbation method. The basic equations are firstly transformed into the equations in a moving coordinate system with the celerity of the negative wave front. The depth and velocity are denoted as the power series of the spatial coordinate of the moving coordinate system. After denoting the time dependent coefficient of each term of the power series as the perturbation expansion with the bottom friction coefficient, all unknown coefficients are derived using the known variables such as the initial depth and gravitational acceleration. The analytical solutions are compared with the numerical results obtained using a Finite Volume Method. Although the results indicate that further investigations are needed to obtain a better analytical solution, it is considered that in this study a mathematical framework is presented to study the asymptotic behavior of the depth distribution with negative infinite gradient at the front position to the Ritter solution when the friction coefficient tends to 0.