Modelling turbulent flow from dam break using slow manifolds

Article


Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2009. "Modelling turbulent flow from dam break using slow manifolds ." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (S), pp. C1033-C1051.
Article Title

Modelling turbulent flow from dam break using slow manifolds

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 Citation50 (S), pp. C1033-C1051
Number of Pages19
Year2009
Place of PublicationCambridge, United Kingdom
ISSN1446-1811
1446-8735
Web Address (URL)http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1466
Abstract

[Abstract]: We present a novel approach based on centre manifold technique to describe the dynamics of the mean turbulent velocity of dam-break flow. We avoid empirical assumptions about the cross-stream profile of the velocity; instead solution is obtained using free surface and bed boundary conditions that accommodate constant turbulent shear as a
nearly neutral mode. We describe the turbulent dynamics across the flow, and identify important factors affecting the turbulent dissipation in the lateral direction. The results are verified against available experimental data.

Keywordsdam break, modelling, slow manifolds
ANZSRC Field of Research 2020419999. Other environmental sciences not elsewhere classified
490199. Applied mathematics not elsewhere classified
490105. Dynamical systems in applications
Public Notes

© Australian Mathematical Society 2009. Open access journal. This publication is copyright. 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. Author's version deposited in accordance with the copyright policy of the publisher.

Byline AffiliationsCommonwealth Scientific and Industrial Research Organisation (CSIRO), Australia
University of Adelaide
Computational Engineering and Science Research Centre
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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.