Equations for Turbulent Flood Waves

Abstract

Long waves in rivers, estuaries and floods are described by the St Venant and Boussinesq equations in classical fluid dynamics. Based on the widely used $k$-$ε$ model for turbulence, we use the techniques of centre manifold theory to show how these classical models can be derived from a unified approach to low-dimensional modelling. The model may be refined to an arbitrary degree of accuracy and predicts interesting interactions between the mean flow and the mean turbulence.