The dynamics of the vertical structure of turbulence in flood flows

Article


Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2007. "The dynamics of the vertical structure of turbulence in flood flows." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 48, pp. C573-C590. https://doi.org/10.0000/anziamj.v48i0.124
Article Title

The dynamics of the vertical structure of turbulence in flood flows

ERA Journal ID43
Article CategoryArticle
AuthorsGeorgiev, D. J. (Author), Roberts, A. J. (Author) and Strunin, D. V. (Author)
Journal TitleAustralian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Journal Citation48, pp. C573-C590
Number of Pages18
Year2007
Place of PublicationAustralia
ISSN1446-1811
1446-8735
Digital Object Identifier (DOI)https://doi.org/10.0000/anziamj.v48i0.124
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 κ-ω 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.

Keywordsdynamical systems; centre manifold technique; k-omega turbulence model; computer algebra
ANZSRC Field of Research 2020401213. Turbulent flows
401204. Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
490409. Ordinary differential equations, difference equations and dynamical systems
Public Notes

© 2007 Austral. Mathematical Soc. This publication is open access. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source.
Presented at: ANZIAM~J. In Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006

Byline AffiliationsComputational Engineering and Science Research Centre
Department of Mathematics and Computing
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Strunin, D. V., Melnik, R. V. N. and Roberts, A. J.. 2001. "Coupled thermomechanical waves in hyperbolic thermoelasticity." Journal of Thermal Stresses. 24 (2), pp. 121-140. https://doi.org/10.1080/01495730150500433
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Ujevic, Nenad and Roberts, A. J.. 2004. "A corrected quadrature formula and applications." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 45 (E), pp. E41-E56.
Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2002. "Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models." Computational Mechanics. 29 (1), pp. 16-26. https://doi.org/10.1007/s00466-002-0311-5
Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2001. "Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena." Mechanics Research Communications. 28 (6), pp. 637-651. https://doi.org/10.1016/S0093-6413(02)00216-1
A holistic finite difference approach models linear dynamics consistently
Roberts, A. J.. 2003. "A holistic finite difference approach models linear dynamics consistently." Mathematics of Computation. 72 (241), pp. 247-262. https://doi.org/10.1090/S0025-5718-02-01448-5
Holistic discretisation ensures fidelity to Burger's equation
Roberts, A. J.. 2001. "Holistic discretisation ensures fidelity to Burger's equation." Applied Numerical Mathematics. 37 (3), pp. 371-396. https://doi.org/10.1016/S0168-9274(00)00053-2
A lubrication model of coating flows over a curved substrate in space
Roy, R. Valery, Roberts, A. J. and Simpson, M. E.. 2002. "A lubrication model of coating flows over a curved substrate in space." Journal of Fluid Mechanics. 454 (1), pp. 235-261. https://doi.org/10.1017/S0022112001007133
Nonlinear instability in generalized nonlinear phase diffusion equation
Strunin, Dmitry V.. 2003. "Nonlinear instability in generalized nonlinear phase diffusion equation." Progress of Theoretical Physics Supplement.
Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids
Roberts, A. J.. 2007. Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids . University of Southern Queensland.
Computer algebra derives normal forms of stochastic differential equations
Roberts, A. J.. 2007. Computer algebra derives normal forms of stochastic differential equations . Toowoomba, Australia. University of Southern Queensland.
Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation
Roberts, A. J.. 2006. Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation. Toowoomba, Australia. University of Southern Queensland.
The style files: favour the present tense
Roberts, Tony. 2006. "The style files: favour the present tense." Gazette of the Australian Mathematical Society. 33 (5), pp. 313-314.
The style files: explicitly avoid false conditionals
Roberts, Tony. 2006. "The style files: explicitly avoid false conditionals." Gazette of the Australian Mathematical Society. 33 (4), pp. 241-242.
The style files: inform with titles, abstracts and introductions
Roberts, Tony. 2006. "The style files: inform with titles, abstracts and introductions." Gazette of the Australian Mathematical Society. 33 (3), pp. 169-170.
The style files: clarify this
Roberts, Tony. 2006. "The style files: clarify this." Gazette of the Australian Mathematical Society. 33 (2), pp. 104-105.
The style files: prefer active writing to passive
Roberts, Tony. 2006. "The style files: prefer active writing to passive." Gazette of the Australian Mathematical Society. 33 (1), pp. 22-23.
Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, A. J.. 2005. Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations. Toowoomba, Australia. University of Southern Queensland.
Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
Roberts, A. J.. 2006. "Resolving the multitude of microscale interactions accurately models stochastic partial differential equations." LMS Journal of Computation and Mathematics. 9, pp. 193-221. https://doi.org/10.1112/S146115700000125X
An accurate and comprehensive model of thin fluid flows with inertia on curved substrates
Roberts, A. J. and Li, Zhenquan. 2006. "An accurate and comprehensive model of thin fluid flows with inertia on curved substrates." Journal of Fluid Mechanics. 553 (1), pp. 33-73. https://doi.org/10.1017/S0022112006008640
Resolve the multitude of microscale interactions to holistically discretise the stochastically forced Burgers' partial differential equation
Roberts, A. J.. 2006. Resolve the multitude of microscale interactions to holistically discretise the stochastically forced Burgers' partial differential equation. Toowoomba, Australia. University of Southern Queensland.
General tooth boundary conditions for equation free modelling
Roberts, A. J. and Kevrekidis, I. G.. 2006. General tooth boundary conditions for equation free modelling. Toowoomba, Australia. University of Southern Queensland.
Attractors and centre manifolds in nonlinear diffusion
Strunin, Dmitry V.. 2005. "Attractors and centre manifolds in nonlinear diffusion." 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asian SIAM Symposium. Hong Kong, China 12 - 16 Dec 2005 Hong Kong.
Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models
Melnik, R. V. N., Strunin, D. V. and Roberts, A. J.. 2005. "Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models." Numerical Heat Transfer Part A: Applications. 47 (6), pp. 549-569. https://doi.org/10.1080/10407780590891236
Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators
Roberts, A. J. and Kevrekidis, I. G.. 2005. "Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators." May, Rob and Roberts, A, J. (ed.) CTAC 2004: 12th Biennial Computational Techniques and Applications Conference. Melbourne, Australia Sep 2004 Cambridge, United Kingdom .
Predicting the off-site deposition of spray drift from horticultural spraying through porous barriers on soil and plant surfaces
Mercer, Geoff and Roberts, Tony. 2005. "Predicting the off-site deposition of spray drift from horticultural spraying through porous barriers on soil and plant surfaces." Wake, Graeme (ed.) MISG 2005: 22nd Mathematics-In-Industry Study Group. Auckland, New Zealand 24 - 28 Jan 2005 Auckland, New Zealand.