Models encompassing hydraulic jumps in radial flows over a horizontal plate

Paper


Strunin, Dmitry and Roberts, Tony. 2001. "Models encompassing hydraulic jumps in radial flows over a horizontal plate." Kluev, Vitaly and Mastorakis, Nikos (ed.) 2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001). Cairns, Australia 17 - 23 Dec 2001 Greece.
Paper/Presentation Title

Models encompassing hydraulic jumps in radial flows over a horizontal plate

Presentation TypePaper
AuthorsStrunin, Dmitry (Author) and Roberts, Tony (Author)
EditorsKluev, Vitaly and Mastorakis, Nikos
Journal or Proceedings TitleProceedings of the 2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001)
Number of Pages6
Year2001
Place of PublicationGreece
ISBN9608052521
Web Address (URL) of Paperhttp://www.wseas.us/e-library/conferences/cairns2001/papers/598.pdf
Conference/Event2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001)
Event Details
2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001)
Event Date
17 to end of 23 Dec 2001
Event Location
Cairns, Australia
Abstract

A circular jump forms in the radial flow thickness when a downwards stream hits a horizontal plate. Centre manifold theory is used to rigorously derive, from the Navier-Stokes equations, a dynamic model for slow horizontal variations of flow thickness and velocity. An advantage of this approach is the capacity to study non-stationary regimes and examine stability of the flow. Numerical solutions of the model reproduce experimentally observed recirculation under the jump and quantitatively agree with experiments of laminar flows.

Keywordsradial fluid flow; hydraulic jump; centre manifold
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
401299. Fluid mechanics and thermal engineering not elsewhere classified
401706. Numerical modelling and mechanical characterisation
Byline AffiliationsDepartment of Mathematics and Computing
Institution of OriginUniversity of Southern Queensland
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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.