# The dynamics of the vertical structure of turbulence in flood flows

Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V. (2006) The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 48 (CTAC-2). C573-C590. ISSN 1446-8735

## Abstract

The flow of water in a tide, flood or tsunami is often turbulent. We model large scale, but shallow, turbulent flow using the well established $k$-$\omega$ model of turbulence. Vertical turbulent mixing underlies the existence of a slow manifold model. As a first step, in this article the flow 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 influence on the mathematical analysis of key physical factors affecting the dynamics: turbulent mixing, energy production due to shear, volume energy dissipation and gravitational forcing on sloping ground. Further research will incorporate large scale lateral variations in the flow in order to predict tides, floods and tsunamis.

Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive See the publisher website for access to full-text: http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/124 Dr Dian Georgiev Historic - Faculty of Sciences - Department of Maths and Computing 11 Dec 2007 00:33 02 Jul 2013 22:55 dynamical systems, centre manifold technique, k-omega turbulence model, computer algebra 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems http://eprints.usq.edu.au/id/eprint/3643