Floods, tides and tsunamis are turbulent, yet conventional models are based
upon depth averaging inviscid irrotational flow equations. We propose to change
the base of such modelling to the Smagorinksi large eddy closure for turbulence
in order to appropriately match the underlying fluid dynamics. Our approach
allows for large changes in fluid depth to cater for extreme inundations. The
key to the analysis underlying the approach is to choose surface and bed
boundary conditions that accommodate a constant turbulent shear as a nearly
neutral mode. Analysis supported by slow manifold theory then constructs a
model for the coupled dynamics of the fluid depth and the mean turbulent
lateral velocity. The model resolves the internal turbulent shear in the flow
and thus may be used in further work to rationally predict erosion and
transport in turbulent floods