ORCID Profile
0000-0003-4679-8663
Current Organisation
Swinburne University of Technology
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Dynamical Systems | Theoretical Physics | Pure Mathematics | Thermodynamics And Statistical Physics | Mathematical Physics | Turbulent Flows
Physical sciences | Behavioural and cognitive sciences | Biological sciences | Earth sciences | Mathematical sciences |
Publisher: Elsevier BV
Date: 12-2008
Publisher: The Royal Society
Date: 13-01-2010
Abstract: In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele–Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.
Publisher: Royal Society of Chemistry (RSC)
Date: 2014
DOI: 10.1039/C4EE02841D
Abstract: A robust separation strategy using novel particle-flow-instability physics is successfully developed for a difficult-to-separate suspension in which there is some combination of a small density difference between solid and liquid, high viscosity, and small-sized particles.
Publisher: American Physical Society (APS)
Date: 07-1992
Publisher: ASME International
Date: 28-04-2021
DOI: 10.1115/1.4050701
Abstract: Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. While the more familiar turbulent flows promote efficient transport and mixing by their inherent spatio-temporal disorder, laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems, and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion (“advection”) and the geometry, topology, and coherence of fluid trajectories. Efficient laminar transport being equivalent to “chaotic advection” is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows, yet the real world is three-dimensional (3D). Second, Lagrangian transport is typically investigated for idealized flows, yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilization of know-how on 3D Lagrangian transport and its dissemination to practice. To this end, 3D practical flows are categorized into canonical problems. First, to expose the ersity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the “Lagrangian mindset” into the analysis and design of 3D practical flows.
Publisher: Springer Berlin Heidelberg
Date: 2001
Publisher: Begellhouse
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 12-2001
Publisher: American Physical Society (APS)
Date: 11-02-2002
Publisher: American Physical Society (APS)
Date: 21-02-2017
Publisher: SPIE
Date: 26-12-2008
DOI: 10.1117/12.815265
Publisher: AIP Publishing
Date: 2006
DOI: 10.1063/1.2163913
Abstract: Reoriented duct flows of generalized Newtonian fluids are an idealization of non-Newtonian fluid flow in industrial in-line mixers. Based on scaling analysis and computation we find that non-Newtonian duct flows have several limit behaviors, in the sense that such flows can become (nearly) independent of one or more of the rheological and dynamical control parameters, simplifying the general flow and mixing problem. These limit flows give several levels of modeling complexity to the full problem of non-Newtonian duct flow. We describe the sets of simplified flow models and their corresponding regions of validity. This flow-model decomposition captures the essential rheological and dynamical characteristics of the reoriented duct flows and enables a more efficient and systematic study and design of flow and mixing of non-Newtonian fluids in ducts. Key aspects of the flow-model decomposition are demonstrated via a specific, but representative, duct flow.
Publisher: Elsevier BV
Date: 1999
Publisher: AIP Publishing
Date: 04-2017
DOI: 10.1063/1.4979666
Abstract: Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes, including mixing, chemical reaction, and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID) however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow. We show that transitions from one-dimensional (1D) to two-dimensional (2D) and 2D to 3D transport occur based on the relative magnitudes of streamline jumps in two transverse directions.
Publisher: Elsevier BV
Date: 10-2015
Publisher: Elsevier BV
Date: 05-2001
Publisher: AIP Publishing
Date: 14-09-2015
DOI: 10.1063/1.4930837
Abstract: Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.
Publisher: WORLD SCIENTIFIC
Date: 03-2010
Publisher: American Physical Society (APS)
Date: 02-05-1994
Publisher: Elsevier BV
Date: 1995
Publisher: AIP Publishing
Date: 10-2006
DOI: 10.1063/1.2359698
Abstract: Tracer advection of non-Newtonian fluids in reoriented duct flows is investigated in terms of coherent structures in the web of tracer paths that determine transport properties geometrically. Reoriented duct flows are an idealization of in-line mixers, encompassing many micro and industrial continuous mixers. The topology of the tracer dynamics of reoriented duct flows is Hamiltonian. As the stretching per reorientation increases from zero, we show that the qualitative route from the integrable state to global chaos and good mixing does not depend on fluid rheology. This is due to a universal symmetry of reoriented duct flows, which we derive, controlling the topology of the tracer web. Symmetry determines where in parameter space global chaos first occurs, while increasing non-Newtonian effects delays the quantitative value of onset. Theory is demonstrated computationally for a representative duct flow, the rotated arc mixing flow.
Publisher: AIP Publishing
Date: 06-2008
DOI: 10.1063/1.2937726
Abstract: When the symmetry of axisymmetric Taylor vortex flow is broken, time-periodic wavy vortex flow (WVF) appears and quite quickly becomes globally chaotic (in the Lagrangian sense) with increasing Reynolds number. Previously published simulations of WVF suggest that beyond a certain Re, nonmixing vortex cores reappear in the flow and grow in size with further increases in Re. This reappearance occurs well into the inertia-dominated flow regime and coincides with a decrease in axial fluid dispersion and an increase in flow symmetry as measured by certain Eulerian symmetry measures. In this brief paper, we present experimental dye-reaction visualization results from two WVF wave states in the region where vortex cores are predicted numerically. The experimental results show unambiguous visual evidence for the existence of vortex cores and provide visual agreement with the numerical results. They are significant in that experimental evidence for these structures in WVF has not been reported before. The results also suggest that vortex-to-vortex transport occurs via sheetlike structures that are pulled from one vortex to another and become wrapped around the vortex cores before being stretched to the point at which molecular diffusion dominates.
Publisher: American Physical Society (APS)
Date: 23-10-2013
Publisher: Elsevier BV
Date: 2012
DOI: 10.1016/J.JCONHYD.2011.04.006
Abstract: Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media. These scalars can be targeted by pump-and-treat methods or by amendment technologies. Application ex les include in-situ leaching for metals, recovery of dissolved contaminant plumes, or utilizing heat energy in geothermal reservoirs. While conventional pumping methods work reasonably well, costs associated with maintaining pumping schedules are high and improvements in efficiency would be welcome. In this paper we discuss how transient switching of the pressure at different wells can intimately control subsurface flow, generating a range of "programmed" flows with various beneficial characteristics. Some programs produce chaotic flows which accelerate mixing, while others create encapsulating flows which can isolate fluid zones for lengthy periods. In a simplified model of an aquifer subject to balanced pumping, chaotic flow topologies have been predicted theoretically and verified experimentally using Hele-Shaw cells. Here, a survey of the key characteristics of chaotic advection is presented. Mathematical methods are used to show how these characteristics may translate into practical situations involving regional flows and heterogeneity. The results are robust to perturbations, and withstand significant aquifer heterogeneity. It is proposed that chaotic advection may form the basis of new efficient technologies for groundwater interventions.
Publisher: Elsevier BV
Date: 12-1996
Publisher: Cambridge University Press (CUP)
Date: 25-01-1996
DOI: 10.1017/S0022112096000122
Abstract: Dilute mixtures of 3 He in superfluid 4 He have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 Pr 2. Moreover, owing to the tight coupling of the temperature and concentration fields, superfluid mixture convection is closely analogous to classical Rayleigh–Bénard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids, well described by the Boussinesq equations. This work has two goals. The first is to put the theory of superfluid mixture convection on a firmer basis. We accomplish this by combining experiment and analysis to measure superfluid effects on the onset of convection. In the process, we demonstrate quantitative control over superfluid effects and, in particular, that deviations from classical convective behaviour can be made small or at worst no larger than finite aspect ratio effects. The size of superfluid effects at convective onset can be less than a few percent for temperatures 1 T 2 K. Comparison of the measured properties of superfluid mixture roll instabilities above the onset of convection (e.g. skewed varicose, oscillatory, and particularly near the codimension-2 point) to the properties predicted by Boussinesq calculations further verifies that superfluid mixtures convect as classical fluids. With superfluid effects understood and under control, the second goal, presented in Part 2, is to exploit the unique Pr range of superfluid mixtures and the variable aspect ratio (Γ) capabilities of our experiment to survey convective instabilities in the broad, and heretofore largely unexplored, parameter space 0.12 Pr 1.4 and 2 Γ 95. The aim is to identify and characterize time-dependence and chaos, and to discover new dynamical behaviour in strongly nonlinear convective flows.
Publisher: The Royal Society
Date: 13-05-2010
Abstract: The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31 , 469–485 ( doi:10.1063/1.866828 )) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.
Publisher: American Physical Society (APS)
Date: 05-1994
Publisher: Elsevier BV
Date: 10-2006
Publisher: World Scientific Pub Co Pte Lt
Date: 06-1993
DOI: 10.1142/S0218127493000581
Abstract: Mixtures of 3 He in superfluid 4 He provide an interesting and important system for testing theories of convection and for studying nonlinear dynamics. Here we describe experimental observations of chaotic bursting in a convecting layer of 3 He -superfluid- 4 He . For aspect ratio Γ=6.0 and Prandtl number Pr=0.3, we find intermittent bursts out of a chaotic state. This state evolved via a series of well-defined transitions involving established routes to chaos. Above the onset of bursting the average length of a burst-free region l varies as a power law: l ∝(R−R b ) −γ with γ=4.6 a power-law dependence of l is expected. An unexpected result is that the average length of a burst varies as (R−R b ) δ with δ=2.0. In addition, a particularly novel state was seen for Γ=4.25 and Pr=0.12, where there occurs a reversible switching transition involving two chaotic attractors.
Publisher: Springer Science and Business Media LLC
Date: 18-07-2001
Publisher: Elsevier BV
Date: 05-2016
Publisher: Elsevier BV
Date: 03-2008
Publisher: Wiley
Date: 06-2019
DOI: 10.1111/GWMR.12339
Publisher: American Physical Society (APS)
Date: 29-04-2010
Publisher: SPIE
Date: 21-12-2008
DOI: 10.1117/12.769348
Publisher: Springer Science and Business Media LLC
Date: 13-09-2019
Publisher: Elsevier BV
Date: 11-2009
Publisher: Wiley
Date: 19-09-2006
DOI: 10.1002/AIC.10640
Publisher: AIP Publishing
Date: 03-2020
DOI: 10.1063/1.5135333
Abstract: Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in such flows through coordination of lower-order and higher-order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant. Degenerate points of periodic lines and the extended 3D structures associated with them are easily identified through the trace of the deformation tensor calculated along periodic lines. These results reveal the importance of degenerate points in understanding transport in one-invariant fluid flows.
Publisher: American Geophysical Union (AGU)
Date: 08-2011
DOI: 10.1029/2011WR010444
Publisher: AIP Publishing
Date: 09-1999
DOI: 10.1063/1.166432
Abstract: Flowing granular materials are complex, industrially important, and scientifically provocative. In this paper we report measurements of granular transport in 3-dimensional tumbling containers. We use magnetic resonance imaging techniques for direct tracking of particles and measure the interior flows of granular materials. One goal is to measure industrial mixer performance over a wide range of conditions. As the mixer geometries are relatively simple, such measurements could serve as incisive tests during development of better granular equations of motion.
Publisher: Elsevier BV
Date: 11-2016
Publisher: American Physical Society (APS)
Date: 14-06-2017
Publisher: Elsevier BV
Date: 04-2001
Publisher: Cambridge University Press (CUP)
Date: 25-01-1996
DOI: 10.1017/S0022112096000134
Abstract: Dilute mixtures of 3 He in superfluid 4 He have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 Pr 2. Moreover, superfluid mixture convection is closely analogous to classical Rayleigh–Bénard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids. This work has two goals. The first, accomplished in Part 1, is to experimentally validate the superfluid mixture convection analogue to Rayleigh–Bénard convection. With superfluid effects understood and under control, the second goal is to identify and characterize time-dependence and chaos and to discover new dynamical behaviour in strongly nonlinear convective flows. In this paper, Part 2, we exploit the unique Pr range of superfluid mixtures and the variable aspect ratio (Γ) capabilities of our experiment to survey convective instabilities in the broad, and heretofore largely unexplored, parameter space 0.12 Pr 1.4 and 2 Γ 95. Within this large parameter space, we have focused on small to moderate Γ and Pr and on large Γ with Pr ≈ 1. The novel behaviour uncovered in the survey includes the following. Changing attractors : at Γ = 6.0 and Pr = 0.3, we observe intermittent bursting destabilizing a fully developed chaotic state. Above the onset of bursting the average length of a burst-free interval and the average length of a burst vary as power laws. At Γ = 4.25 and Pr = 0.12 we observe a particularly novel reversible switching transition involving two chaotic attractors. Instability competition : near the codimension-2 point at the crossing of the skewed-varicose and oscillatory instabilities we find that the effects of instability competition greatly increase the complexity and multiplicity of states. A heat-pulse method allows selection of the active state. Decreasing Γ suppresses the available complexity. Superfluid turbulence : we find that the large- litude noisy states, previously believed due to superfluid turbulence, are confined to small values of Γ and Pr and are not consistent with superfluid turbulence. Changing instabilities : at Pr = 0.19 a wavevector detuning changes the type of secondary instability from oscillatory to saddle-node, with an unusual 3/4 exponent time scaling. Very large Γ: at Pr = 1.3 for Γ increasing from 44 to 90, we observe the onset of convection changing from ordered and stationary to disordered and time-dependent. At the beginning of the crossover there are hysteretic transitions to coherent oscillations close to the onset of convection. By the end of the crossover convection is time-dependent and irregular at onset with the fluctuation litude correlated with the mean Nusselt number.
Publisher: American Physical Society (APS)
Date: 14-08-2014
Publisher: AIP Publishing
Date: 02-2016
DOI: 10.1063/1.4941851
Abstract: Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations—such as shear banding or wall slip—creates new mechanisms for mixing and transport beyond those predicted by classical dynamical systems theory. Here, we show how a novel mixing mechanism combining stretching with cutting and shuffling yields exponential mixing rates, quantified by a positive Lyapunov exponent, an impossibility for systems with cutting and shuffling alone or bounded systems with stretching alone, and demonstrate it in a fluid flow. While dynamical systems theory provides a framework for understanding mixing in smoothly deforming media, a theory of discontinuous mixing is yet to be fully developed. New methods are needed to systematize, explain, and extrapolate measurements on systems with discontinuous deformations. Here, we investigate “webs” of Lagrangian discontinuities and show that they provide a template for the overall transport dynamics. Considering slip deformations as the asymptotic limit of increasingly localised smooth shear, we also demonstrate exactly how some of the new structures introduced by discontinuous deformations are analogous to structures in smoothly deforming systems.
Publisher: American Physical Society (APS)
Date: 21-09-2009
Publisher: Elsevier BV
Date: 05-1997
Publisher: Royal Society of Chemistry (RSC)
Date: 2018
DOI: 10.1039/C8NR06367B
Abstract: The integration of acoustic micromixing and single bead trapping enables the identification of fluorescent signals from multiple biomarkers within minutes.
Publisher: Royal Society of Chemistry (RSC)
Date: 2017
DOI: 10.1039/C6LC01263A
Abstract: An integrated device with nanoparticle assay and chaotic micromixing for rapid detection of Hendra virus antibodies.
Publisher: Springer Science and Business Media LLC
Date: 10-2020
Publisher: SPIE
Date: 26-12-2008
DOI: 10.1117/12.814431
Publisher: American Physical Society (APS)
Date: 08-12-1997
Publisher: Springer Science and Business Media LLC
Date: 28-06-2022
Publisher: Elsevier BV
Date: 04-2016
Publisher: Geological Society of London
Date: 09-2001
Abstract: This study aims to establish evidence for the widespread existence of preserved high-resolution trace element variations in speleothems that may have climatic significance. Ion microprobe analysis of speleothems reveals that annual to sub-annual variations in element chemistry exist at five, shallow western European cave sites (Crag Cave, County Kerry and Ballynamintra, County Waterford, Ireland Uamh an Tartair, Sutherland, Scotland Grotte Pere-Noël, Belgium Grotta di Ernesto, NE Italy) with widely varying climatic, geomorphic and geological settings. The variations are not restricted to species (Mg, Sr and Ba) known to substitute directly for Ca in the calcite lattice, but include H, F, Na and P. Phosphorus (as phosphate) displays the greatest variability and may have the most significance as a proxy for the seasonal temperature cycle because of its role as a nutrient element. The technique allows estimation of growth rate of speleothems at any interval of interest, which is one of several possible uses in palaeoclimatology.
Publisher: Springer Netherlands
Date: 1997
Publisher: Elsevier BV
Date: 10-2016
Publisher: Elsevier BV
Date: 12-1998
Publisher: American Physical Society (APS)
Date: 25-09-2018
Publisher: The Royal Society
Date: 13-01-2010
Abstract: The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties.
Publisher: American Geophysical Union (AGU)
Date: 02-2020
DOI: 10.1029/2019WR025982
Abstract: In a recent paper (Trefry et al., 2019, 0.1029/2018wr023864 ), we showed that the interplay of aquifer heterogeneity and poroelasticity can produce complex transport in tidally forced aquifers, with significant implications for solute transport, mixing, and reaction. However, what was unknown was how broadly these transport dynamics can arise in natural groundwater systems and how these dynamics depend upon the aquifer properties and tidal and regional flow characteristics. In this study we answer these questions through parametric studies of these governing properties. We uncover the mechanisms that govern complex transport dynamics and the bifurcations between transport structures that depend upon changes in the governing parameters, and we determine the propensity for complex dynamics to occur in natural aquifer systems. These results clearly demonstrate that complex transport structures and dynamics may arise in natural tidally forced aquifers around the world, producing solute transport and mixing behavior that is very different to that of the conventional Darcy flow picture.
Publisher: Elsevier BV
Date: 06-2001
Publisher: Springer Science and Business Media LLC
Date: 15-09-1999
Publisher: Elsevier BV
Date: 12-2018
Publisher: Springer Science and Business Media LLC
Date: 08-2001
Publisher: Wiley
Date: 06-1998
Publisher: Public Library of Science (PLoS)
Date: 18-07-2018
Publisher: Springer Science and Business Media LLC
Date: 15-10-2010
Publisher: American Geophysical Union (AGU)
Date: 04-2019
DOI: 10.1029/2018WR023864
Publisher: Cambridge University Press (CUP)
Date: 10-02-2002
DOI: 10.1017/S0022112001006917
Abstract: By experiments and supporting computations we investigate two methods of transport enhancement in two-dimensional open cellular flows with inertia. First, we introduce a spatial dependence in the velocity field by periodic modulation of the shape of the wall driving the flow this perturbs the steady-state streamlines in the direction perpendicular to the main flow. Second, we introduce a time dependence through transient acceleration–deceleration of a flat wall driving the flow surprisingly, even though the streamline portrait changes very little during the transient, there is still significant transport enhancement. The range of Reynolds and Reynolds–Strouhal numbers studied is 7.7[les ] Re [les ]46.5 and 0.52[les ] ReSr [les ]12.55 in the spatially dependent mode and 12[les ] Re [les ]93 and 0.26[les ] ReSr [les ]5.02 in the time-dependent mode. The transport is described theoretically via lobe dynamics. For both modifications, a curve with one maximum characterizes the various transport enhancement measures when plotted as a function of the forcing frequency. A qualitative analysis suggests that the exchange first increases linearly with the forcing frequency and then decreases as 1/ Sr for large frequencies.
Publisher: Cambridge University Press (CUP)
Date: 25-06-1994
DOI: 10.1017/S0022112094001539
Abstract: A complex Stokes flow has several cells, is subject to bifurcation, and its velocity field is, with rare exceptions, only available from numerical computations. We present experimental and computational studies of two new complex Stokes flows: a vortex mixing flow and multicell flows in slender cavities. We develop topological relations between the geometry of the flow domain and the family of physically realizable flows we study bifurcations and symmetries, in particular to reveal how the forcing protocol's phase hides or reveals symmetries. Using a variety of dynamical tools, comparisons of boundary integral equation numerical computations to dye advection experiments are made throughout. Several findings challenge commonly accepted wisdom. For ex le, we show that higher-order periodic points can be more important than period-one points in establishing the advection template and extended regions of large stretching. We demonstrate also that a broad class of forcing functions produces the same qualitative mixing patterns. We experimentally verify the existence of potential mixing zones for adiabatic forcing and investigate the crossover from adiabatic to non-adiabatic behaviour. Finally, we use the entire array of tools to address an optimization problem for a complex flow. We conclude that none of the dynamical tools alone can successfully fulfil the role of a merit function however, the collection of tools can be applied successively as a dynamical sieve to uncover a global optimum.
Publisher: Elsevier BV
Date: 08-1991
Publisher: Springer Science and Business Media LLC
Date: 04-03-2012
Publisher: Springer Science and Business Media LLC
Date: 1993
DOI: 10.1007/BF00682012
Publisher: American Physical Society (APS)
Date: 04-07-1994
Publisher: AIP Publishing
Date: 05-2016
DOI: 10.1063/1.4950763
Abstract: Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Publisher: American Geophysical Union (AGU)
Date: 04-1995
DOI: 10.1029/95GL00056
Location: Australia
Start Date: 12-2003
End Date: 12-2004
Amount: $10,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 07-2004
End Date: 06-2009
Amount: $1,500,000.00
Funder: Australian Research Council
View Funded Activity