ORCID Profile
0000-0002-9135-3594
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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)
Astronomical and Space Sciences | Mathematical Physics | Biomedical Engineering | Medical Physics | Mathematical Sciences Not Elsewhere Classified | Biomedical Engineering Not Elsewhere Classified | Seismology and Seismic Exploration | Mathematics Not Elsewhere Classified | Applied Mathematics | Geophysics | Broadband Network Technology | Atmospheric Sciences | Optimisation | Operations Research | Numerical Analysis | Quantum Chemistry | Environmental Engineering | Ship And Platform Hydrodynamics | Navigation And Position Fixing | Stellar Astronomy and Planetary Systems | Environmental Engineering Modelling | Glaciology | Climatology (Incl. Palaeoclimatology) | Groundwater Hydrology | Numerical Solution of Differential and Integral Equations | Theoretical and Applied Mechanics | Petroleum And Reservoir Engineering | Astronomy And Astrophysics | Galactic Astronomy | Astronomical and Space Instrumentation
ANZSRC Socio-Economic Objective (SEO)
Medical instrumentation | Physical sciences | Scientific instrumentation | Mathematical sciences | Expanding Knowledge in the Physical Sciences | Education and training not elsewhere classified | Organic industrial chemicals not classified elsewhere | Land and water management | Climate Variability (excl. Social Impacts) | Nautical equipment | Climate change | Land and water management | Land and water management | Information services not elsewhere classified | Other | Expanding Knowledge in the Earth Sciences | Expanding Knowledge in the Mathematical Sciences |
Related Links
Publications
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
Rayleigh–Taylor Flow with Two Interfaces: The Completed Boussinesq Approximation
Publisher: Springer Science and Business Media LLC
Date: 30-10-2023
Evolution of H II regions in hierarchically structured molecular clouds
Publisher: Oxford University Press (OUP)
Date: 11-10-2006
Using the Spatial Population Abundance Dynamics Engine for conservation management
Publisher: Wiley
Date: 11-08-2015
FULLY 3D RAYLEIGH–TAYLOR INSTABILITY IN A BOUSSINESQ FLUID
Publisher: Cambridge University Press (CUP)
Date: 07-2019
DOI: 10.1017/S1446181119000087
Abstract: Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.
Large-Amplitude Elastic Free-Surface Waves: Geometric Nonlinearity and Peakons
Publisher: Springer Science and Business Media LLC
Date: 26-08-2021
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.
WARF: A Weighted-Sum Approach to Radial MRI Image Reconstruction With a Rotating RF Coil
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2020
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.
Modelling competition between hybridising subspecies
Publisher: Elsevier BV
Date: 02-2020
DOI: 10.1016/J.JTBI.2019.110072
Abstract: The geographic niches of many species are dramatically changing as a result of environmental and anthropogenic impacts such as global climate change and the introduction of invasive species. In particular, genetically compatible subspecies that were once geographically separated are being reintroduced to one another. This is of concern for conservation, where rare or threatened subspecies could be bred out by hybridising with their more common relatives, and for commercial interests, where the stock or quality of desirable harvested species could be compromised. It is also relevant to disease ecology, where disease transmission is heterogeneous among subspecies and hybridisation may affect the rate and spatial spread of disease. We develop and investigate a mathematical model to combine competitive effects via the Lotka-Volterra model with hybridisation effects via mate choice. The species complex is structured into two classes: a subspecies of interest (named x), and other subspecies including any hybrids produced (named y). We show that in the absence of limit cycles the model has four possible equilibrium outcomes, representing every combination: total extinction, x-dominance (y extinct), y-dominance (x extinct), and at most a single coexistence equilibrium. We give conditions for which limit cycles cannot exist, then further show that the "total extinction" equilibrium is always unstable, that y-dominance is always stable, and that the other equilibria have stability depending on the model parameters. We demonstrate that both x-dominance and coexistence are achievable under a wide range of parameter values and initial conditions, which corresponds with empirical evidence of known competing-hybridising systems. We then briefly examine bifurcation behaviour. In particular, we note that a subcritical bifurcation is possible in which a "catastrophic" transition from x-dominance to y-dominance can occur, representing an invasion event. Finally, we briefly examine the common complication of time-varying carrying capacity, showing that such a case can make coexistence more likely.
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
An analytic simplification for the reconstruction problem of electrical impedance tomography
Publisher: Wiley
Date: 2002
DOI: 10.1002/IMA.10008
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.
Chemical Kinetics of a Bipalladium Complex
Publisher: American Chemical Society (ACS)
Date: 10-01-2013
DOI: 10.1021/JP310368G
Abstract: A theoretical model is presented, for reductive elimination in a bipalladium complex, based on the model of Ariafard et al. (2011). This reaction is of particular interest due to the novel Pd(III) intermediate. A thermo-kinetic model is proposed for this reaction scheme, and the rate laws and energy balance are given as a system of ordinary differential equations. A simplified model is then derived that only involves two key variables, so that the system can be analyzed completely in a phase plane. It is shown that kinetic oscillations do not occur, but that there are multiple steady states for the reaction. These new features are confirmed by a numerical analysis of the full model scheme. The predictions provide a mechanism to test the model and the underlying computational chemistry.
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.
Planetary waves in polar basins: Some exact solutions
Publisher: Elsevier BV
Date: 07-2021
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
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.
Rotating gravitational lenses: a kinematic approach
Publisher: Oxford University Press (OUP)
Date: 10-09-2014
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
A comparison of explicit Runge-Kutta methods
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 19-03-2023
DOI: 10.21914/ANZIAMJ.V64.17438
Abstract: Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here. doi: 10.1017/S1446181122000141
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
Unsteady free surface flow induced by a line sink in a fluid of finite depth
Publisher: Elsevier BV
Date: 03-2008
Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity
Publisher: Cambridge University Press (CUP)
Date: 25-06-2002
DOI: 10.1017/S0022112002008510
Abstract: The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.
Steady flow of a buoyant plume into a constant-density layer
Publisher: Springer Science and Business Media LLC
Date: 22-09-2009
Closed-form approximation for supersonic flow over a cone
Publisher: Springer Science and Business Media LLC
Date: 11-12-2019
Analytic and numerical solutions to the seismic wave equation in continuous media
Publisher: The Royal Society
Date: 11-2020
Abstract: This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial condition of sufficient symmetry, this provides a valuable check for the validity of the numerical method that follows. A particular initial condition is found which allows for a new closed-form solution. A numerical scheme is then presented which combines a spectral (Fourier) representation for displacement components and wave-speed parameters, a fourth-order Runge–Kutta integration method, and an absorbing boundary layer. The resulting large system of differential equations is solved in parallel on suitable enhanced performance desktop hardware in a new software implementation. This provides an alternative approach to forward modelling of waves within isotropic media which is efficient, and tailored to rapid and flexible developments in modelling seismic structure, for ex le, shallow depth environmental applications. Visual comparisons of the analytic solution and the numerical scheme are presented.
A Note on the Overall Magnification of a Gravitational Point-Source—Point-Lens System
Publisher: Cambridge University Press (CUP)
Date: 2015
DOI: 10.1017/PASA.2015.46
Abstract: The total magnification due to a point lens has been of particular interest as the theorem that gravitational lensing results in light lification for all observers appears to contradict the conservation of photon number. This has been discussed several times, and various resolutions have been offered. In this note, we use a kinematic approach to provide a formula for the magnification factor for the primary image accurate to first order and valid for rays leaving the source at any trajectory. We thus determine the magnification over a sphere surrounding the system. A new result found is that while the magnification dips below unity far from the optical axis as noted by others, it returns to unity directly behind the source.
Optimal fluid injection strategies for in situ mineral leaching in two-dimensions
Publisher: Springer Science and Business Media LLC
Date: 1999
COUETTE FLOW OVER A HEAT ISLAND
Publisher: Cambridge University Press (CUP)
Date: 2023
DOI: 10.1017/S1446181123000032
Abstract: A viscous fluid is confined between two smooth horizontal walls, in a vertical channel. The upper wall may move with constant speed, but the lower wall is stationary and a portion of it is heated. A plume of heated fluid develops, and may also be swept downstream by the motion of the upper wall. When the heating effect is small and the upper plate does not move, a closed-form solution for the temperature profile is presented. A numerical spectral method is then presented, and allows highly accurate nonlinear solutions to be obtained, for the temperature and the fluid motion. These are compared against the closed-form solution in the linearized case, and the effects of nonlinearity on temperature and velocity are revealed. The results also show that periodic plume shedding from the heated region can occur in the nonlinear case.
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.
The Rayleigh–Taylor instability in a porous medium
Publisher: Springer Science and Business Media LLC
Date: 23-01-2021
DOI: 10.1007/S42452-021-04160-Z
Abstract: The classical Rayleigh–Taylor instability occurs when a heavy fluid overlies a lighter one, and the two fluids are separated by a horizontal interface. The configuration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar flow, but in a porous medium governed by Darcy’s law. First, the fully saturated situation is considered, where the two horizontal fluids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely diffuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding flow for two free fluids.
A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration
Publisher: Oxford University Press (OUP)
Date: 14-09-2010
A comparison of two- and three-variable models for combustion in sealed containers
Publisher: Cambridge University Press (CUP)
Date: 04-2006
DOI: 10.1017/S1446181100010117
Abstract: This paper analyses a model for combustion of a self-heating chemical (such as pool chlorine), stored in drums within a shipping container. The system is described by three coupled nonlinear differential equations for the concentration of the chemical, its temperature and the temperature within the shipping container. Self-sustained oscillations are found to occur, as a result of Hopf bifurcation. Temperature and concentration profiles are presented and compared with the predictions of a simpler two-variable approximation for the system. We study the period of oscillation and its variation with respect to the ambient temperature and the reaction parameter. Nonlinear resonances are found to exist, as the solution jumps between branches having different periods.
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.
A model for the treatment of environmentally transmitted sarcoptic mange in bare-nosed wombats (Vombatus ursinus)
Publisher: Elsevier BV
Date: 02-2019
DOI: 10.1016/J.JTBI.2018.11.033
Abstract: Some of the most important wildlife diseases involve environmental transmission, with disease control attempted via treatments that induce temporary pathogen resistance among hosts. However, theoretical explanations of such circumstances remain few. A mathematical model is proposed and investigated to analyse the dynamics and treatment of environmentally transmitted sarcoptic mange in a population of bare-nosed wombats. The wombat population is structured into four classes representing stages of infection, in a model that consists of five non-linear differential equations including the unattached mite population. It is shown that four different epidemiological outcomes are possible. These are: (1) extinction of wombats (and mites) (2) mite-free wombat populations (3) endemic wombats and mites coexisting, with the wombats' population reduced below the environmental carrying capacity and (4) a stable limit cycle (sustained oscillating populations) with wombat population far below carrying capacity. Empirical evidence exists for the first two of these outcomes, with the third highly likely to occur in nature, and the fourth plausible at least until wombat populations succumb to Allee effects. These potential outcomes are examined to inform treatment programs for wombat populations. Through this theoretical exploration of a relatively well understood empirical system, this study supports general learning across environmentally transmitted wildlife pathogens, increasing understanding of how pathogen dynamics may cause crashes in some populations and not others.
Flow due to a sink near a vertical wall, in infinitely deep fluid
Publisher: Elsevier BV
Date: 07-2005
FULLY 3D FLUID OUTFLOW FROM A SPHERICAL SOURCE
Publisher: Cambridge University Press (CUP)
Date: 04-2022
DOI: 10.1017/S1446181122000098
Abstract: We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated.
Fully 3D Fluid Outflow From a Spherical Source
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 28-08-2022
DOI: 10.21914/ANZIAMJ.V64.17015
Abstract: We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated. doi: 10.1017/S1446181122000098
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
A Simple and Practical Algorithm for Accurate Gravitational Magnification Maps
Publisher: Cambridge University Press (CUP)
Date: 2017
DOI: 10.1017/PASA.2016.62
Abstract: In this brief communication, a new method is outlined for modelling magnification patterns on an observer’s plane using a first-order approximation to the null geodesic path equations for a point mass lens. For each ray emitted from a source, an explicit calculation is made for the change in position on the observer’s plane due to each lens mass. By counting the number of points in each small area of the observer’s plane, the magnification at that point can be determined. This allows for a very simple and transparent algorithm. A short Matlab code s le for creating simple magnification maps due to multiple point lenses is included in an appendix.
Salt-water up-coning during extraction of fresh water from a tropical island
Publisher: Springer Science and Business Media LLC
Date: 2004
AXISYMMETRIC PLUMES IN VISCOUS FLUIDS
Publisher: Cambridge University Press (CUP)
Date: 04-2019
DOI: 10.1017/S1446181119000075
Abstract: We consider fluid in a channel of finite height. There is a circular hole in the channel bottom, through which fluid of a lower density is injected and rises to form a plume. Viscous boundary layers close to the top and bottom of the channel are assumed to be so thin that the viscous fluid effectively slips along each of these boundaries. The problem is solved using a novel spectral method, in which Hankel transforms are first used to create a steady-state axisymmetric (inviscid) background flow that exactly satisfies the boundary conditions. A viscous correction is then added, so as to satisfy the time-dependent Boussinesq Navier–Stokes equations within the fluid, leaving the boundary conditions intact. Results are presented for the “lazy” plume, in which the fluid rises due only to its own buoyancy, and we study in detail its evolution with time to form an overturning structure. Some results for momentum-driven plumes are also presented, and the effect of the upper wall of the channel on the evolution of the axisymmetric plume is discussed.
The initiation of a planar fluid plume beneath a rigid lid
Publisher: Springer Science and Business Media LLC
Date: 20-01-2017
A note on a linearized approach to gravitational lensing
Publisher: Oxford University Press (OUP)
Date: 08-08-2011
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
Instability of a dense seepage layer on a sloping boundary
Publisher: Cambridge University Press (CUP)
Date: 14-01-2020
Computing unstable periodic waves at the interface of two inviscid fluids in uniform vertical flow
Publisher: Elsevier BV
Date: 2007
An extended Boussinesq theory for interfacial fluid mechanics
Publisher: Springer Science and Business Media LLC
Date: 24-03-2022
DOI: 10.1007/S10665-022-10215-W
Abstract: Boussinesq theory can model quite accurately viscous flows that involve multiple fluids with interfaces between them, so long as there is not much difference between the densities of the various fluids. However, the Boussinesq approximation is generally poor when the density ratio between the fluids is large. Here, we propose an Extended Boussinesq approximate equation, that allows for large density ratios, while still remaining straightforward to implement. Ex les are given for planar Rayleigh–Taylor instability, where the Boussinesq and the novel Extended Boussinesq models are compared with the predictions of an SPH fluid dynamics code, to confirm this approach.
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.
Unsteady free-surface flow induced by a line sink
Publisher: Springer Science and Business Media LLC
Date: 2003
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.
A COMPARISON OF EXPLICIT RUNGE-KUTTA METHODS
Publisher: Cambridge University Press (CUP)
Date: 07-2022
DOI: 10.1017/S1446181122000141
Abstract: Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here.
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