  Consider the dynamics of turbulent flow in rivers, estuaries and floods.
Based on the widely used k-epsilon model for turbulence, we use the techniques
of centre manifold theory to derive dynamical models for the evolution of the
water depth and of vertically averaged flow velocity and turbulent parameters.
This new model for the shallow water dynamics of turbulent flow: resolves the
vertical structure of the flow and the turbulence; includes interaction between
turbulence and long waves; and gives a rational alternative to classical models
for turbulent environmental flows.
