The dynamics of the vertical structure of turbulence in flood flows

Abstract

The ow of water in a tide, ood or tsunami is often turbulent. We model large scale, but shallow, turbulent ow using the well estab- lished κ-ω model of turbulence. Vertical turbulent mixing underlies the existence of a slow manifold model. As a first step, in this arti- cle the ow is assumed laterally homogeneous. Then constructing the slow manifold discovers the evolution of the average lateral velocity and average turbulent energy. We focus upon the inuence on the mathematical analysis of key physical factors affiecting the dynamics: turbulent mixing, energy production due to shear, volume energy dis- sipation and gravitational forcing on sloping ground. Further research will incorporate large scale lateral variations in the ow in order to predict tides, oods and tsunamis.