Author(s): A. L. Le Fessant; D. Dartus; J. Chorda
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Keywords: Free surface flow; Instabilities; Obstacles; Signal analysis
Abstract: The aim of this study is the diagnostic, through experimental and numerical approaches, of instabilities phenomenon observed on steep rough slope. Experiments on water flume reveal the occurrence of undulations of the free surface above a bottom with equidistant barriers which allows an increase of the roughness. Several configurations of parameters have been studied: relative barriers spacing, slope, flow rate. It allows to observing several types of regimes. Then, we could verify the control of the waves train due to the relative spacing between the barriers, and also the apparition of others two-dimensional instabilities. In order to understand these phenomena, we propose a model based on the two dimensional shallow water equations, where the friction terms are given by the Strickler formula. A numerical code is developed in order to validate our approach. It is based on a total variation diminishing (TVD) scheme, allowing the exact resolution of discontinuities. Boundary conditions are specified by Thomson's method, which is based on the method of characteristics and the analysis of the different waves crossing the domain boundary. The final objective of this work to provide a code that would be able to restitute the development of observed instabilities. Therefore, we compare numerical and experimental results. This comparison is based on spectral, correlation and wavelet analysis. It will be possible to propose theoretical criteria for various configurations and to identify instabilities triggers.
Year: 2001