Remi A. Carmigniani1,†, Michel Benoit2, Damien Violeau3 and Morteza Gharib4 1Saint-Venant Hydraulics Laboratory, Joint Research Unit EDF – Cerema – Ecole des Ponts, 78401 Chatou, France 2Institut de Recherche sur les Phénomènes Hors-Equilibre (IRPHE, UMR 7342), Aix-Marseille Université, CNRS, Centrale Marseille, 13013 Marseille, France 3EDF and Saint-Venant Hydraulics Laboratory, Joint Research...

Negative surges are caused by a sudden change in flow resulting from a decrease in water depth. New experiments were conducted in a horizontal channel (L = 12 m, W = 0.5 m) to record the unsteady water depth and turbulence in negative surges. The data were collected using video imagery, acoustic displacement meters and acoustic Doppler velocimetry (ADV). The experimental setup was designed to r...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

From several results in recent years, starting with Hörmander’s characterization of the constant coefficient partial differential equations P (D)u = f that have a real analytic solution u for every real analytic function f , it has become clear that certain properties of the partial differential operator P (D) are equivalent to estimates of Phragmén–Lindelöf type for plurisubharmonic functions ...

We investigate a version of the Phragmén–Lindelöf theorem for solutions of the equation ∆∞u = 0 in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the p-harmonic equation when p tends to ∞.

This paper describes a numerical scheme for approximate the viscous Saint-Venant equations. This scheme is called staggered grid scheme which is a robust, simple and strightforward scheme for viscous SaintVenant equations. Some numerical simulations have been elaborated to validate the accuracy of the scheme, such as the calculation of the convergence rate L1-norm error of the scheme, the compa...