Martin Rentschler

An exact solution for ideal dam-break floods on steep slopes

Dam-break floods on steep slopes occur in diverse settings. They may result from failure of either natural or man-made dams, and they have been responsible for the loss of thousands of lives [Costa, 1988]. Recent disasters resulting from dam-break floods on steep slopes include those at Fonte Santa mines, Portugal, in November 2006 and Taum Sauk, Missouri, USA, in December 2005. Numerical solutions of the shallow-water equations are generally used to predict the behavior of dam-break floods, but exact analytical solutions suitable for testing these numerical solutions have been available only for floods with infinite volumes, horizontal beds, or both. Computational models used to simulate dam-break floods commonly produce numerical instabilities and/or significant errors close to the moving front when steep slopes and/or irregular terrain are present in the flood path. In part these problems reflect the complex interaction of phenomena not included in model formulation (e.g., intense sediment transport under timedependent flow conditions), but in part they also reflect shortcomings in the numerical solution algorithms themselves. Therefore it is important to obtain exact analytical solutions of the shallow-water equations that can be used to test the robustness of numerical models when they are applied to floods of finite volume on steep slopes. This paper presents a new solution for this purpose.

Front dynamics of supercritical non-Boussinesq gravity currents.

In this paper, we seek similarity solutions to the shallow water (Saint-Venant) equations for describing the motion of a non-Boussinesq, gravity-driven current in an inertial regime. The current is supplied in fluid by a source placed at the inlet of a horizontal plane. Gratton and Vigo (1994) found similarity solutions to the Saint-Venant equations when a Benjamin-like boundary condition was imposed at the front (i.e., nonzero flow depth); the Benjamin condition represents the resisting effect of the ambient fluid for a Boussinesq current (i.e., a small-density mismatch between the current and the surrounding fluid). In contrast, for non-Boussinesq currents the flow depth is expected to be zero at the front in absence of friction. In this paper, we show that the Saint-Venant equations also admit similarity solutions in the case of non-Boussinesq regimes provided that there is no shear in the vertical profile of the streamwise velocity field. In that case, the front takes the form of an acute wedge with a straight free boundary and is separated from the body by a bore.

Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case

We report the developments of hydrodynamic instabilities in several well-balanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight the need of low dissipative high-order well-balanced filter schemes for non-equilibrium flows with variable cut-off wavenumber to compute the out-balance flow under consideration, i.e. the kinematic wave.