ORCID Profile
0000-0002-5812-6015
Current Organisation
Murdoch University
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Numerical Solution of Differential and Integral Equations | Theoretical and Applied Mechanics | Applied Mathematics | Mathematical Sciences Not Elsewhere Classified | Mathematical Physics | Optimisation | Operations Research | Petroleum And Reservoir Engineering | Environmental Engineering | Environmental Engineering Modelling | Groundwater Hydrology |
ANZSRC Socio-Economic Objective (SEO)
Education and training not elsewhere classified | Land and water management | Land and water management | Land and water management | Other | Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Mathematical Sciences | Mathematical sciences
Related Links
Publications
Critical and supercritical withdrawal from a two-layer fluid through a line sink in a partially bounded aquifer
Publisher: Elsevier BV
Date: 12-2009
Algorithm for Selective Withdrawal from Stratified Reservoir
Publisher: American Society of Civil Engineers (ASCE)
Date: 07-1988
On starting conditions for a submerged sink in a fluid
Publisher: Springer Science and Business Media LLC
Date: 16-08-2007
A NOTE ON STEADY FLOW INTO A SUBMERGED POINT SINK
Publisher: Cambridge University Press (CUP)
Date: 10-2014
DOI: 10.1017/S1446181114000303
Abstract: The steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.
On the computation of steady axi-symmetric withdrawal from a two-layer fluid
Publisher: Elsevier BV
Date: 03-2003
Modelling microbial pollutant loads associated with surface water run-off in water supply catchments
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 15-04-2018
Dense underflow into a lake or reservoir—Sub-critical flow.
Publisher: Elsevier BV
Date: 06-2017
Quasi‐Two‐Dimensional Reservoir Simulation Model
Publisher: American Society of Civil Engineers (ASCE)
Date: 09-1991
NUMERICAL ANALYSIS OF APPARATUS-INDUCED DISPERSION FOR DENSITY-DEPENDENT SOLUTE TRANSPORT IN POROUS MEDIA
Publisher: Cambridge University Press (CUP)
Date: 2023
Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary
Publisher: Springer Science and Business Media LLC
Date: 1995
DOI: 10.1007/BF00046379
Unsteady flow induced by a withdrawal point beneath a free surface
Publisher: Cambridge University Press (CUP)
Date: 10-2005
DOI: 10.1017/S1446181100009986
Abstract: The unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.
An intrusion layer in stationary incompressible fluids: Part 1: Periodic waves
Publisher: Cambridge University Press (CUP)
Date: 10-2006
DOI: 10.1017/S0956792506006693
Abstract: Waves on a neutrally buoyant intrusion layer moving into otherwise stationary fluid are studied. There are two interfacial free surfaces, above and below the moving layer, and a train of waves is present. A small litude linearized theory shows that there are two different flow types, in which the two interfaces are either in phase or else move oppositely. The former flow type occurs at high phase speed and the latter is a low-speed solution. Nonlinear solutions are computed for large litude waves, using a spectral type numerical method. They extend the results of the linearized analysis, and reveal the presence of limiting flow types in some circumstances.
IDEAL PLANAR FLUID FLOW OVER A SUBMERGED OBSTACLE: REVIEW AND EXTENSION
Publisher: Cambridge University Press (CUP)
Date: 10-2021
DOI: 10.1017/S1446181121000341
Abstract: A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour.
Unsteady plumes in planar flow of viscous and inviscid fluids
Publisher: Oxford University Press (OUP)
Date: 07-09-2011
Withdrawal of a fluid of finite depth through a line sink with a cusp in the free surface
Publisher: Elsevier BV
Date: 09-1998
Steady flow of a jet of fluid from an angled slot impacting on a horizontal wall
Publisher: Springer Science and Business Media LLC
Date: 30-11-2021
A note on withdrawal from a fluid of finite depth through a point sink
Publisher: Cambridge University Press (CUP)
Date: 10-2002
DOI: 10.1017/S1446181100013882
Abstract: The problem of withdrawal through a point sink of water from a fluid of finite depth with a free surface is considered. Assuming the flow to be axisymmetric, it is found that there is a maximum Froude number at which such flows can exist. This maximum corresponds to the formation of a secondary stagnation ring on the free surface. This result extends earlier work on this problem. Comparison is made with a small Froude number solution and past experimental results.
INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES
Publisher: Cambridge University Press (CUP)
Date: 2012
DOI: 10.1017/S1446181112000156
Abstract: The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.
Unsteady flows induced by a point source or sink in a fluid of finite depth
Publisher: Cambridge University Press (CUP)
Date: 22-07-2016
DOI: 10.1017/S0956792516000310
Abstract: The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.
Waveless subcritical flow past symmetric bottom topography
Publisher: Cambridge University Press (CUP)
Date: 09-11-2012
DOI: 10.1017/S0956792512000381
Abstract: The subcritical flow of a stream over a bottom obstruction or depression is considered with particular interest in obtaining solutions with no downstream waves. In the linearised problem this can always be achieved by superposition of multiple obstructions, but it is not clear whether this is possible in a full nonlinear problem. Solutions computed here indicate that there is an effective nonlinear superposition principle at work as no special shape modifications were required to obtain wave-cancelling solutions. Waveless solutions corresponding to one or more trapped waves are computed at a range of different Froude numbers and are shown to provide a rather elaborate mosaic of solution curves in parameter space when both negative and positive obstruction heights are included.
Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth
Publisher: Cambridge University Press (CUP)
Date: 10-02-2001
DOI: 10.1017/S0022112000002780
Abstract: The steady response of a fluid consisting of two regions of different density, the lower of which is of finite depth, is considered during withdrawal. Super-critical flows are considered in which water from both layers is being withdrawn, meaning that the interface is drawn down directly into the sink. The results indicate that if the flow rate is above some minimum, the angle of entry of the interface depends more strongly on the relative depth of the sink than on the flow rate. This has quite dramatic consequences for the understanding of selective withdrawal from layered fluids.
A line sink in a flowing stream with surface tension effects
Publisher: Cambridge University Press (CUP)
Date: 30-10-2015
DOI: 10.1017/S0956792515000546
Abstract: We examine a problem in which a line sink causes a disturbance to an otherwise uniform flowing stream of infinite depth. We consider the fully non-linear problem with the inclusion of surface tension and find the maximum sink strength at which steady solutions exist for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension.
Potential flow of fluid from an elevated, two-dimensional source
Publisher: Elsevier BV
Date: 07-2019
Unsteady draining of a fluid from a circular tank
Publisher: Elsevier BV
Date: 12-2010
The lens of freshwater in a tropical island––2d withdrawal
Publisher: Elsevier BV
Date: 2004
DISPERSAL OF HYDROGEN IN THE RETINA—A THREE-LAYER MODEL
Publisher: Cambridge University Press (CUP)
Date: 2022
DOI: 10.1017/S1446181122000050
Abstract: Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.
AN EXAMINATION OF THE “LANIER WING” DESIGN
Publisher: Cambridge University Press (CUP)
Date: 2023
DOI: 10.1017/S1446181123000068
Abstract: Six patents were secured by E. H. Lanier from 1930 to 1933 for aeroplane designs that were intended to be exceptionally stable. A feature of five of these was a flow-induced “vacuum chamber” which was thought to provide superior stability and increased lift compared to typical wing designs. Initially, this chamber was in the fuselage, but later designs placed it in the wing by replacing a section of the upper skin of the wing with a series of angled slats. We report upon an investigation of the Lanier wing design using inviscid aerodynamic theory and viscous numerical simulations. This took place at the 2005 Australia–New Zealand Mathematics-in-Industry Study Group. The evidence from this investigation does not support the claims but, rather, suggests that any improvement in lift and/or stability seen in the few prototypes that were built was, most probably, due to thicker airfoils than were typical at the time.
The effect of surface tension on free-surface flow induced by a point sink
Publisher: Cambridge University Press (CUP)
Date: 18-03-2016
DOI: 10.1017/S1446181116000018
Abstract: The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.
A note on waveless subcritical flow past symmetric bottom topography
Publisher: Cambridge University Press (CUP)
Date: 26-10-2016
DOI: 10.1017/S0956792516000449
Abstract: This paper re-examines the problem of the flow of a fluid of finite depth over two Gaussian-shaped obstructions on the stream bed. A weakly nonlinear analysis in the form of the Korteweg–de Vries equation is used to compare with the results of the fully nonlinear problem. The main focus is to find waveless subcritical solutions, and contours showing the obstruction height and separation values that result in waveless solutions are found for different Froude numbers and different obstruction widths.
Editorial
Publisher: Cambridge University Press (CUP)
Date: 2010
Supercritical withdrawal from a two-layer fluid through a line sink
Publisher: Cambridge University Press (CUP)
Date: 25-08-1995
DOI: 10.1017/S0022112095002990
Abstract: Accurate numerical solutions to the problem of finding the location of the interface between two unconfined regions of fluid of different density during the withdrawal process are presented. Supercritical flows are considered, in which the interface is drawn directly into the sink. As the flow rate is reduced, the interface enters the sink more steeply, until the solution method breaks down just before the interface enters the sink vertically from above, and becomes flow from the lower layer only. This lower bound on supercritical flow is compared with the upper bound on single-layer (free surface) flow with good agreement.
A model of flow in a sugar diffuser
Publisher: Oxford University Press (OUP)
Date: 25-04-2016
The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth
Publisher: Elsevier BV
Date: 10-2017
Dense underflow into a lake or reservoir – supercritical flow solutions
Publisher: Elsevier BV
Date: 02-2017
Subcritical free-surface flow caused by a line source in a fluid of finite depth
Publisher: Springer Science and Business Media LLC
Date: 11-1992
DOI: 10.1007/BF00042763
CRITICAL SURFACE CONING DUE TO A LINE SINK IN A VERTICAL DRAIN CONTAINING A POROUS MEDIUM
Publisher: Cambridge University Press (CUP)
Date: 07-2019
DOI: 10.1017/S1446181119000099
Abstract: The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.
Critical surface coning due to a line sink in a vertical drain containing a porous medium
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 08-09-2019
DOI: 10.21914/ANZIAMJ.V61I0.13434
Abstract: The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history. doi:10.1017/S1446181119000099
Unsteady free surface flow induced by a line sink in a fluid of finite depth
Publisher: Elsevier BV
Date: 03-2008
Steady flow of a buoyant plume into a constant-density layer
Publisher: Springer Science and Business Media LLC
Date: 22-09-2009
Extraction of density-layered fluid from a porous medium
Publisher: Springer Science and Business Media LLC
Date: 28-06-2022
DOI: 10.1007/S10665-022-10229-4
Abstract: We consider axisymmetric flow towards a point sink from a stratified fluid in a vertically confined aquifer. We present two approaches to solve the equations of flow for the linear density gradient case. Firstly, a series method results in an eigenfunction expansion in Whittaker functions. The second method is a finite difference method. Comparison of the two methods verifies the finite difference method is accurate, so that more complicated nonlinear, density stratification can be considered. Interesting results for the case where the density stratification changes from linear to almost two-layer are presented, showing that in the nonlinear stratification case, there are certain values of flow rate for which a steady solution does not occur. A spectral method is then implemented to consider cases in which there is a stagnant region beneath a sharp interface between two layers of different, but constant, density. In this situation, flows also exist only for flow rates beneath a critical flux value, consistent with the results for the continuous density stratification.
Flow of non-Newtonian fluids in open channels
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 15-05-2018
The effect of gravity on flow past a semi-circular cylinder with a constant pressure wake
Publisher: Elsevier BV
Date: 05-2008
Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth
Publisher: Springer Science and Business Media LLC
Date: 25-02-2022
DOI: 10.1007/S10665-022-10211-0
Abstract: The two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, $$x_\\mathrm{{s}} 1$$ x s 1 , there is only one stagnation point on the surface, at the wall. However, if the horizontal location $$x_{\\mathrm{s}} 1$$ x s 1 , a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.
A note on the flow of a homogeneous intrusion into a two-layer fluid
Publisher: Cambridge University Press (CUP)
Date: 04-2007
DOI: 10.1017/S0956792507006924
Abstract: The intrusion of a constant density fluid at the interface of a two-layer fluid is considered. Numerical solutions are computed for a model of a steady intrusion resulting from flow down a bank and across a broad lake or reservoir. The incoming fluid is homogeneous and spreads across the lake at its level of neutral buoyancy. Solutions are obtained for a range of different inflow angles, flow rate and density differences. Except in extreme cases, the nature of the solution is predicted quite well by linear theory, with the wavelength at any Froude number given by a dispersion relation and wave steepness determined largely by entry angle. However, some extreme solutions with rounded meandering flows and non-unique solutions in the parameter space are also obtained.
Control of algal blooms in reservoirs with a curtain: a numerical analysis
Publisher: Elsevier BV
Date: 2001
Extraction of density-layered fluid from a porous medium
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-07-2020
DOI: 10.21914/ANZIAMJ.V61I0.14996
Abstract: We consider axisymmetric flow towards a point sink from a stratified fluid in a vertically confined aquifer. We present two approaches to solve the equations of flow for the linear density gradient case. Firstly, a series method results in an eigenfunction expansion in Whittaker functions. The second method is a simple finite difference method. Comparison of the two methods verifies the finite difference method is accurate, so that more complicated nonlinear, density stratification can be considered. Such nonlinear profiles cannot be considered with the eigenfunction approach. Interesting results for the case where the density stratification changes from linear to almost two-layer are presented, showing that in the nonlinear case there are certain values of flow rate for which a steady solution does not occur. References Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 9th ed. National Bureau of Standards, Washington, 1972. Bear, J. and Dagan, G. Some exact solutions of interface problems by means of the hodograph method. J. Geophys. Res. 69(8):1563–1572, 1964. doi:10.1029/JZ069i008p01563 Bear, J. Dynamics of fluids in porous media. Elsevier, New York, 1972. 486656756.html COMSOL Multiphysics. COMSOL Multiphysics Programming Reference Manual, version 5.3. .3/doc/com.comsol.help.comsol/COMSOL_ProgrammingReferenceManual.pdf Farrow, D. E. and Hocking, G. C. A numerical model for withdrawal from a two layer fluid. J. Fluid Mech. 549:141–157, 2006. doi:10.1017/S0022112005007561 Henderson, N., Flores, E., S aio, M., Freitas, L. and Platt, G. M. Supercritical fluid flow in porous media: modelling and simulation. Chem. Eng. Sci. 60:1797–1808, 2005. doi:10.1016/j.ces.2004.11.012 Lucas, S. K., Blake, J. R. and Kucera, A. A boundary-integral method applied to water coning in oil reservoirs. ANZIAM J. 32(3):261–283, 1991. doi:10.1017/S0334270000006858 Meyer, H. I. and Garder, A. O. Mechanics of two immiscible fluids in porous media. J. Appl. Phys., 25:1400–1406, 1954. doi:10.1063/1.1721576 Muskat, M. and Wycokoff, R. D. An approximate theory of water coning in oil production. Trans. AIME 114:144–163, 1935. doi:10.2118/935144-G GNU Octave. oftware/octave/doc/v4.2.1/ Yih, C. S. On steady stratified flows in porous media. Quart. J. Appl. Maths. 40(2):219–230, 1982. doi:10.1090/qam/666676 Yu, D., Jackson, K. and Harmon, T. C. Disperson and diffusion in porous media under supercritical conditions. Chem. Eng. Sci. 54:357–367, 1999. doi:10.1016/S0009-2509(98)00271-1 Zhang, H. and Hocking, G. C. Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface. J. Eng. Math. 32:365–376, 1997. doi:10.1023/A:1004227232732 Zhang, H., Hocking, G. C. and Seymour, B. Critical and supercritical withdrawal from a two-layer fluid through a line sink in a bounded aquifer. Adv. Water Res. 32:1703–1710, 2009. doi:10.1016/j.advwatres.2009.09.002 Zill, D. G. and Wright, W. S. Differential Equations with Boundary-value problems, 8th Edition. Brooks Cole, Boston USA, 2013.
Modelling hydrogen clearance from the retina
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 04-04-2018
A note on withdrawal from a two-layer fluid through a line sink in a porous medium
Publisher: Cambridge University Press (CUP)
Date: 07-2008
Modelling of hydrogen diffusion in the retina
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-07-2020
DOI: 10.21914/ANZIAMJ.V61I0.14995
Abstract: A simple mathematical model for diffusion of hydrogen within the retina has been developed. The model consists of three, well-mixed, one dimensional layers that exchange hydrogen via a diffusion process. A Fourier series method is applied to compute the hydrogen concentration. The effect of important parameters is examined and discussed. The results may contribute to an understanding of the hydrogen clearance technique to estimate blood flow. A two dimensional numerical method for the hydrogen diffusion is also presented. It is shown that the predominant features of the process are captured quite well by the simpler model. References V. A. Alder, D. Y. Yu, S. J. Cringle and E. N. Su. Experimental approaches to diabetic retinopathy. Asia-Pac. J. Ophthalmol. 4:20–25, 1992. J. C. Arciero, P. Causin and F. Malgoroli. Mathematical methods for modeling the microcirculation. AIMS Biophys. 4:362–399, 2017. doi:10.3934/biophy.2017.3.362 D. E. Farrow, G. C. Hocking, S. J. Cringle and D.-Y. Yu. Modeling Hydrogen clearance from the retina. ANZIAM J. 59:281–292, 2018. doi:10.1017/S1446181117000426 A. B. Friedland. A mathematical model of transmural transport of oxygen to the retina. Bull. Math. Biol. 40:823–837, 2018 doi:10.1007/BF02460609 D. Goldman. Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15:795–811, 2008. doi:10.1080/10739680801938289 A. C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers. In Scientific Computing, R. S. Stepleman, et al., Eds., pp. 55-64. North-Holland, Amsterdam, 1983. S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–41, 1951. ontent/3/1/1 B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19:59–98, 1979. doi:10.1016/0045-7825(79) 90034-3 S. L. Mitchell. Coupling transport and chemistry: numerics, analysis and applications. PhD thesis, University of Bath, UK, 2003. researchportal.bath.ac.uk/en/studentTheses/coupling-transport-and-chemistry-numerics-analysis-and-applicatio G. A. Winchell. Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat. Master\\textquoteright s Thesis, Northwestern University, Evanston, USA, 1983. ermalink/f/5c25nc/01NWU_ALMA21563278530002441 D. Y. Yu, V. A. Alder and S. J. Cringle. Measurement of blood flow in rat eyes by hydrogen clearance. Am. J. Physiol. (Heart Circ. Physiol.) 261:H960–H968, 1991. doi:10.1152/ajpheart.1991.261.3.H960 D. Y. Yu, S. J. Cringle, V. A. Alder, E. N. Su, and P. K. Yu, Intraretinal oxygen distribution and choroidal regulation in the avascular retina of guinea pigs. Am. J. Physiol. (Heart Circ. Physiol.) 270:H965-H973, 1996. doi:10.1152/ajpheart.1996.270.3.H965 S. Cringle, D.-Y. Yu, V. Alder, E.-N. Su, and P. Yu. Choroidal regulation of oxygen supply to the guinea pig retina. In A. G. Hudetz, and D. F. Bruley (Eds.), Oxygen Transport to Tissue XX, pp. 385–389. Springer, 1998. doi:10.1007/978-1-4615-4863-8
Withdrawal from Two‐Layer Fluid Through Line Sink
Publisher: American Society of Civil Engineers (ASCE)
Date: 06-1991
Editorial
Publisher: Cambridge University Press (CUP)
Date: 07-2010
Flow induced by a line sink near a vertical wall in a fluid with a free surface, Part II: finite depth
Publisher: Springer Science and Business Media LLC
Date: 21-04-2022
DOI: 10.1007/S10665-022-10217-8
Abstract: Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink.
An intrusion layer in stationary incompressible fluids Part 2: A solitary wave
Publisher: Cambridge University Press (CUP)
Date: 10-2006
DOI: 10.1017/S0956792506006711
Abstract: The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg–de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces.
Flow due to a sink near a vertical wall, in infinitely deep fluid
Publisher: Elsevier BV
Date: 07-2005
A spectral modelling approach for fluid flow into a line sink in a confined aquifer
Publisher: Cambridge University Press (CUP)
Date: 11-2022
DOI: 10.1017/S0956792521000310
Abstract: A spectral method is developed to study the steady and unsteady flow of fluid into a line sink from a horizontally confined aquifer, and the results are compared to solutions obtained implementing the finite element package COMSOL TM . The aquifer or drain is considered to be confined below so that the solutions are fundamentally unsteady. Comparison is made between the two methods in determining the drawdown of the surface.
Comment on “Experimental observations of saltwater up-coning”
Publisher: Elsevier BV
Date: 02-2012
Ideal planar fluid flow over a submerged obstacle: Review and extension
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 31-12-2021
DOI: 10.21914/ANZIAMJ.V63.16571
Abstract: A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341
Models for the effect of rising water in abandoned mines on seismic activity
Publisher: Elsevier BV
Date: 07-2015
A Note on Axisymmetric Supercritical Coning in a Porous Medium
Publisher: Cambridge University Press (CUP)
Date: 04-2014
DOI: 10.1017/S1446181114000170
Abstract: The steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.
MODELLING HYDROGEN CLEARANCE FROM THE RETINA
Publisher: Cambridge University Press (CUP)
Date: 2018
DOI: 10.1017/S1446181117000426
Abstract: The human retina is supplied by two vascular systems: the highly vascular choroidal, situated behind the retina and the retinal, which is dependent on the restriction that the light path must be minimally disrupted. Between these two circulations, the avascular retinal layers depend on diffusion of metabolites through the tissue. Oxygen supply to these layers may be threatened by diseases affecting microvasculature, for ex le diabetes and hypertension, which may ultimately cause loss of sight. An accurate model of retinal blood flow will therefore facilitate the study of retinal oxygen supply and, hence, the complications caused by systemic vascular disease. Here, two simple models of the blood flow and exchange of hydrogen with the retina are presented and compared qualitatively with data obtained from experimental measurements. The models capture some interesting features of the exchange and highlight effects that will need to be considered in a more sophisticated model and in the interpretation of experimental results.
Salt-water up-coning during extraction of fresh water from a tropical island
Publisher: Springer Science and Business Media LLC
Date: 2004
Flow from a source above a sloping base
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 23-06-2020
DOI: 10.21914/ANZIAMJ.V61I0.14988
Abstract: We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3
The initiation of a planar fluid plume beneath a rigid lid
Publisher: Springer Science and Business Media LLC
Date: 20-01-2017
Dispersal of hydrogen in the retina – a three-layer model
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 28-06-2022
DOI: 10.21914/ANZIAMJ.V64.16720
Abstract: Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model. doi: 0.1017/S1446181122000050
Modelling tracer dispersal and residence time in a reservoir
Publisher: Elsevier BV
Date: 07-1994
Coning during withdrawal from two fluids of different density in a porous medium
Publisher: Springer Science and Business Media LLC
Date: 20-01-2009
A note on waveless subcritical flow past a submerged semi-ellipse
Publisher: Springer Science and Business Media LLC
Date: 13-02-2013
Withdrawal from the lens of freshwater in a tropical island: The two interface case
Publisher: Elsevier BV
Date: 11-2011
Draining under gravity in steel galvanization.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 14-06-2020
DOI: 10.21914/ANZIAMJ.V61I0.15155
Abstract: The problem of the coating of steel has been considered in several Mathematics in Industry study groups. In this process, after passing through a bath of molten alloy, steel sheeting is drawn upward to allow draining under gravity and stripping using an air knife, leaving a coating of desirable thickness. Here we discuss some aspects of the problem and in particular the gravity draining component. The problem is a very nice introduction to industrial modelling for students, but is also relevant for manufacturing. References Elsaadawy, E. A., Hanumanth, G. S., Balthazaar, A. K. S., McDermid, J. R., Hrymak, A. N. and Forbes, J.F. ``Coating weight model for the continuous hot-dip galvanizing process'', Metal. Mat. Trans. B, 38:413–424, 2007. doi:10.1007/s11663-007-9037-2 Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Roberts M. ``Coating Deformation in the jet stripping process'' in Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, Eds. T. Marchant, M. Edwards, G. Mercer. Wollongong, Austealia, 2010. documents.uow.edu.au/content/groups ublic/@web/@inf/@math/documents/doc/uow073330.pdf Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Breward, C. ``Deformations arising during air-knife stripping in the galvanization of steel'', in Progress in Industrial Mathematics at ECMI 2010, Eds. M. Gunther, A. Bartel, M. Brunk, S. Schops, M. Striebel. Mathematics in Industry 17, pp. 311-317. Springer, Berlin Heidelberg, 2011. doi:10.1007/978-3-642-25100-9_36 Hocking, G. C., Lavalle, G., Novakovic, R., O'Kiely, D., Thomson, S., Mitchell, S. J., Herterich, R. ``Bananas–-defects in the jet stripping process''. Proceedings of the European Study Group with Industry in Mathematics and Statistics Research Collection. Rome Italy, 2016. researchrepository.ucd.ie/handle/10197/10215 Howison, S. D. and King, J. R. ``Explicit solutions to six free-boundary problems to fluid flow and diffusion''. IMA J. Appl. Math. 42:155–175, 1989. doi:10.1093/imamat/42.2.155 Hocking, G. C., Sweatman, W., Fitt, A. D. and Breward, C. ``Deformations during jet-stripping in the galvanizing process''. J. Eng. Math. Tuck Special Issue, 70:297–306, 2011. doi:10.1007/s10665-010-9394-8 Thornton, J. A. and Graff, H. F. ``An analytical description of the jet-finishing process for hot-dip metallic coatings on strip''. Metal. Mat. Trans. B, 7:607–618, 1976. doi:10.1007/BF02698594 Tuck, E. O. ``Continuous coating with gravity and jet stripping''. Phys. Fluids, 26(9):2352–2358, 1983. doi:10.1063/1.864438 Tuck, E. O., Bentwich, M., and van der Hoek, J. ``The free boundary problem for gravity-driven unidirectional viscous flows''. IMA J. Appl. Math. 30:191–208, 1983. doi:10.1093/imamat/30.2.191
Fluid inflow from a source on the base of a channel
Publisher: Springer Science and Business Media LLC
Date: 21-12-2021
A numerical model for withdrawal from a two-layer fluid
Publisher: Cambridge University Press (CUP)
Date: 08-02-2006
Analysis of continuous and pulsed pumping of a phreatic aquifer
Publisher: Elsevier BV
Date: 02-1999
Unsteady free-surface flow induced by a line sink
Publisher: Springer Science and Business Media LLC
Date: 2003
Unsteady draining flows from a rectangular tank
Publisher: AIP Publishing
Date: 08-2007
DOI: 10.1063/1.2759891
Abstract: Two-dimensional, unsteady flow of a two-layer fluid in a tank is considered. Each fluid is inviscid and flows irrotationally. The lower, denser fluid flows with constant speed out through a drain hole of finite width in the bottom of the tank. The upper, lighter fluid is recharged at the top of the tank, with an input volume flux that matches the outward flux through the drain. As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole. However, waves are present at the interface, and they have a strong effect on the time at which the interface is first drawn into the drain. A linearized theory valid for small extraction rates is presented. Fully nonlinear, unsteady solutions are computed by means of a novel numerical technique based on Fourier series. For impulsive start of the drain, the nonlinear results are found to agree with the linearized theory initially, but the two theories differ markedly as the interface approaches the drain and nonlinear effects dominate. For wide drains, curvature singularities appear to form at the interface within finite time.
Critical withdrawal from a two-layer fluid through a line sink
Publisher: Springer Science and Business Media LLC
Date: 02-1991
DOI: 10.1007/BF00036598
Steady free surface flows induced by a submerged ring source or sink
Publisher: Cambridge University Press (CUP)
Date: 24-01-2012
DOI: 10.1017/JFM.2011.551
Abstract: The steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than $\\rho = \\sqrt{2} $ , there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond $\\rho = \\sqrt{2} $ , a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source ( $\\rho = 0$ ) to those due to a line sink/source ( $\\rho \\ensuremath{\\rightarrow} \\infty $ ). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.
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