Equations for Turbulent Flood Waves

TL;DR

This paper derives simplified models for turbulent flood waves using centre manifold theory, linking classical fluid dynamics equations with turbulence modeling, and predicts interactions between flow and turbulence.

Contribution

It introduces a unified low-dimensional modeling approach for turbulent flood waves based on classical equations and turbulence models.

Findings

Models can be refined to arbitrary accuracy

Predicts interactions between mean flow and turbulence

Provides a unified derivation of classical and turbulence models

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 $k$-$\epsilon$ 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.