Equations for Turbulent Flood Waves

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.