University of Nottingham

13 – 16 July 2009

Acknowledgements

The Organising Committee of the EPFDC 2009 gratefully acknowledges generous financial support from the European Mechanics Society (EUROMECH), the London Mathematical Society (LMS) and the Institute of Mathematics and its Applications (IMA), as well as talk and poster prizes from Springer.

We would like to thank Professors Patrick Huerre (École Polytechnique), John Billingham and Oliver Jensen (University of Nottingham) for their encouragement and support. We are grateful for the kind help and care of the School of Mathematical Sciences at the University of Nottingham in hosting this year's meeting, in particular, Mrs Helen Cunliffe for her patience and helpful advice, Mrs Hilary Lonsdale for administrative assistance, and we are in debt to Mrs Andrea Blackbourn and Mr Dave Parkin for financial and technical guidance respectively.

We also owe thanks to our supervisors for letting us devote some time to make this conference possible. It would be, however, unfair to say that we could have managed this event without the enthusiasm and assistance of our European Organising Committee: Steve Metcalfe, Simon Pearce (Keele University, EPFDC organisers 2008) and James Sprittles (Birmingham University, EPFDC organiser 2007). Last but not least, we appreciate the efforts of the Nottingham Hospitality Department and Ms Diana Nesbitt (Nottingham Conferences) for ensuring that our time here in the “Robin Hood County” is most enjoyable.

Finally, we thank all our delegates and invited plenary speakers for their valuable contributions to making the conference a success, for welcoming the goals of EPFDC and maintaining the high standard of the meeting.

Zofia Jones, Igor Chernyavsky, Oliver Bain, Leah Band

University of Nottingham

July 2009

Conference Information

Accommodation and Venues

Registration takes place from 11am until about 1pm in room A20 in the Pope Building (No.27 on the map). The room is adjacent to the ground floor west entrance of the building, close to the George Green library. Luggage can be securely stored in this room before the transfer to accommodation at the end of day.

The main conference venue is room Pope C19. The poster sessions and lunches are located in room Coates C28. The main conference accommodation is at Hugh Stewart Hall, which is a 5 minute walk from the main venue. Breakfasts and evening meals are served in the Hall. The Conference Dinner will also be held at Hugh Stewart Hall on Wednesday 15th July starting from 7pm.

Delegates are asked to check-out on Thursday 16th July after breakfast and return their keys to reception before going to the conference. Luggage can be kept in Pope A20 until departure. Those staying in Derby Hall on Thursday or Sunday will need to check in there separately for the additional nights, and of course return their key the following morning to Derby Hall reception.

According to national law, the University operates a no-smoking policy both in academic buildings and in halls. Delegates should familiarise themselves with the emergency procedures and location of emergency exits. In the unlikely event of an accident, assistance is available: Please contact the Organising Committee, or for more serious accidents call the University 24 hour Emergency Service 01159 518888 (internal call: 8888). The Pope building fire alarm is tested each week and will ring for 10 seconds on Wednesday at approximately 11:00am.

Campus Facilities

An Internet Access Point and telephone are provided in each room of the halls of residence. Delegates bringing laptops are advised to bring a standard Ethernet cable for connection. Additionally, there are free wireless access points around the academic buildings, allowing use of the network, UoN-Guest, for all participants. Please follow instructions on http:// www.nottingham.ac.uk/is/uon-wireless/ andhttp://www.nottingham.ac.uk/is/uon-wireless/wireless_guides/wireless_Guest_setup.php.

There are numerous shops, cash machines and other services in the Portland Building (No. 15 on the map), which is less than 10 minutes walk from both Hugh Stewart Hall and the conference venues.

Presentation and Poster Guidelines

Each talk should last 15 minutes, allowing for 5 minutes of questions. Delegates are asked to load their presentations to the local computer before the start of the session. An overhead projector is also available.

Posters should be placed in room Coates C28 during lunch on Monday 13th July and remain in place until the end of the conference. Stick pads will be provided. On Tuesday morning, we have a short session in which delegates are encouraged to present a one-minute summary of their poster.

Conference Programme

Monday 13th July

11:00am – 1:10pm Registration and Buffet LunchPope A20

1:20pm – 1:30pm Welcome and AnnouncementsPope C19

1:30pm - 2:30pm Plenary Lecture: Prof. Andrew Fowler

2:40pm – 3:20pm

2:40pm 3:00pm

Environmental Flows

Madeleine GoldingChristian Klettner

3:25pm – 4:45pm

3:25pm3:45pm4:05pm4:25pm

Non-Newtonian Flows

Oliver BainSusanne ClausMatthew HamerErnst Hoeschele

4:45pm – 5:10pm Coffee Break

5:10pm – 5:50pm

5:10pm5:30pm

Heat and Mass Transfer

Kamil KwiatkowskiAnuhar Osorio-Nesme

5:50pm Transfer to Accommodation

7:00pm – 8:00pm Evening Meal

Tuesday 14th July

7:30am – 9:00am Breakfast in Halls

9:20am – 10:20am

9:20am9:40am10:00am

Computational Fluid Dynamics and Experimental Techniques I

Michal KoperaValerio IungoBoon Tee

10:30am – 10:40am One Minute Poster Summary

10:40am – 11:40am Poster Session and CoffeeCoates C28

11:40am – 12:40pm

11:40pm12:00pm12:20pm

Computational Fluid Dynamics and Experimental Techniques II

Daniel HartmannAndre NicolleRodolphe Prignitz

12:40pm – 1:30pm Lunch

1:30pm – 2:30pm Plenary Lecture: Prof. David Quéré

2:35pm – 3:35pm

2:35pm2:55pm3:15pm

Thin Films and Interface Phenomena I

James SprittlesAlice ThompsonSergii Veremieiev

3:40pm – 6:00pm Trip to Wollaton Park and/or Nottingham Castle

7:00pm – 8:00pm Evening Meal

Wednesday 15th July

7:30am – 9:00am Breakfast in Halls

9:00am – 9:40am

9:00am9:20am

Thin Films and Interface Phenomena II

Georgy KitavtsevIoan Vancea

9:45am – 10:25am

9:45am 10:05am

Biofluids I

Igor ChernyavskyAdriana Setchi

10:25am – 10:50am Coffee Break

10:50am – 11:50am

10:50am11:10am11:30am

Biofluids II

Zuhaila IsmailDarren KnoxShahrzad Nayebossadri

11:50am – 12:40pm Question and Answer Session with Plenary Speakers

12:40pm – 1:30pm Lunch

1:30pm – 2:30pm Plenary Lecture: Prof. Timothy Pedley

2:40pm – 4:00pm

2:40pm3:00pm3:20pm3:40pm

Flow Instabilities I

Arsalan AhmadChristopher GurneySebastian RemmlerAbdul Samad

7:00pm – 9:00pm Conference Dinner

Thursday 16th July

7:30am – 9:00am Breakfast in Halls

9:20am – 10:20am

9:20am9:40am10:00am

Flow Instabilities II

Vladimir ParezanovicPeter StewartFlorencia Tettamanti

10:20am – 11:20am Poster Session and Coffee

11:30am – 12:30pm Plenary Lecture: Prof. Jacques Magnaudet

12:30pm – 12:40pm Concluding Remarks

12:40pm – 1:30pm Lunch

A B S T R A C T S

Plenary Lectures

Prof. Andrew Fowler (OCIAM, University of Oxford)

Sub-glacial Fluid Mechanics

Glaciers are huge, slowly moving rivers of ice which deform in the manner of a slowviscous fluid, and which are themselves often underlain by water which flows in a varietyof hydraulic regimes. Glacier flow is capable of some surprising behaviour, much ofit dictated by the role of water beneath the glacier. The talk will describe some ofthese phenomena, and will then describe how it is thought that subglacial water flow isinstrumental in determining how such behaviour can occur.

Prof. Jacques Magnaudet (Institut de Mecanique des Fluides de Toulouse)

Wake and Path Instabilities of Rising Bubbles

The zigzag or helical path followed by millimetric air bubbles rising in a glass of water ispart of everyday experience. Despite the apparent simplicity of this physical arrangement,understanding the mechanism leading to this non-straight path has been a long-standingproblem in fluid mechanics for various practical and theoretical reasons. This talk willshow that this toy problem is actually an archetype of the way a light, freely-movingbody and its wake interact. Il will also give the opportunity to discuss in a generic waythe conditions under which the wake past a bluff body becomes unstable, irrespective ofthe slip or no-slip boundary condition at the body surface.

Prof. Timothy J. Pedley (DAMTP, University of Cambridge)

Individual and Collective Behaviour in Suspensions of Swimming

Micro-organisms

Bioconvection patterns are observed in shallow suspensions of randomly, but on averageupwardly, swimming micro-organisms which are a little denser than water. The basicmechanism is that an overturning instability develops when the upper regions of fluidbecome denser than the lower regions. The reason for the upswimming depends onthe species of micro-organism: certain algae are bottom-heavy, and therefore experiencea gravitational torque when they are not vertical; certain oxytactic bacteria swim up

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oxygen gradients that they generate by consuming oxygen. Rational continuum modelscan be formulated and analysed in each of these cases, as long as the cell volume fractionis low enough for cell-cell interactions to be neglected. An important aspect of the theoryis the stress distribution associated with the cells’ active swimming motions, and theeffect depends on whether they are ‘pullers’ (like algae) or ‘pushers’ (like bacteria).

Another sort of pattern-formation (“whorls and jets”) is observed in very concentratedcultures of swimming bacteria where cell-cell interactions are crucial. Here we examinethe deterministic swimming of model organisms which interact hydrodynamically butdo not exhibit intrinsic randomness except in their initial positions and orientations. Amicro-organism is modelled as a squirming, inertia-free sphere with prescribed tangentialsurface velocity. Pairwise interactions have been computed using the boundary elementmethod, and the results stored in a database. The movement of a number of identicalsquirmers is computed by the Stokesian Dynamics method, with the help of the databaseof interactions. It is found that the spreading in three dimensions is correctly described asa diffusive process after a sufficiently long time. Scaling arguments are used to estimatethis time-scale and the diffusivities. These depend strongly on volume fraction and modeof squirming. However, in two dimensions the squirmers show a definite tendency toaggregation.

Prof. David Quere (ESPCI, Paris)

Self-Propelling Drops

We first recall classical results on wetting, going back to Pliny, Leidenfrost, Young andLaplace. Then, we discuss the behaviour of liquid drops when they are placed in asym-metric landscapes of energy. In some (favourable) cases, this triggers a spontaneousmotion of the drop. In other ones, pinning on the solid surfaces make the drop resist anymotion. We discuss strategies to overcome this difficulty.

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Talks

Ahmad, A., Cater, J., Avital, E., & Lawn, C.

Experimental Aeroacoustics Study on Jet Noise Reduction Using

Tangential Air Injection

Aircraft jet exhausts are a source of undesirable noise and continue to be an area ofinvestigation driven by increasingly stringent regulation. The noise is produced by theunsteady mixing of the jet with the surrounding air and is dominated by the effects ofthe shear layer. In this study, unheated jets of Mach 1.3 are used to achieve the sameconvective Mach number commonly found in civil aircraft jet exhausts and measurementsare taken to explore the effects of a tangential flow component generated through twodistinct injection methods. The first technique consists of tangential flow injectors locatedupstream of the nozzle exit whereas the second involves an equal number of control jetsspaced further downstream around the nozzle exit. Acoustic measurements were madein an anechoic chamber equipped with an array of 10 free-field microphones whilst localflow field conditions were observed using Particle Image Velocimetry (PIV). Althoughboth forms of tangential injection allowed for reductions in sound pressure levels (SPL)at a range of observer angles, external injection was found to be more efficient throughachieving similar noise reductions at only a fraction of the injection mass flow ratio. Themost significant example was at the sideline angle noise spectra which shows an 18dBreduction that totally eliminated both broadband shock and screech noise at a Strouhalnumber of 0.75, however at the expense of increased high frequency noise beyond St=2.Current research is aimed at investigating an effectively mass-less synthetic jet injectionsystem for noise reduction. The ultimate objective is to develop a configuration thatrequires minimal air injection for maximum noise reduction whilst minimising weightand thrust penalties.

Bain, O. & Billingham, J.

Gravity-Driven Flows of Granular Materials

Studies relevant to granular materials have been in progress at least since de Coulomb’swork in 1776, and are applicable to research areas including geophysical flows, astro-physics, engineering research and chemical and pharmaceutical work. This project islooking at the flow of granular materials within cone-type crushing machines, on behalfof our sponsor.

The dynamics of granular materials are little understood, and there are many proposedmodels for use in different circumstances, types of medium, and length scale. We areusing the continuum model proposed by Jop, Forterre and Pouliquen (Nature 441, 2006),and are modelling two-dimensional channel and chute flows of granular material withgeometry of varying complexity.

Cone crusher machines refine coarsely processed material into a better quality forimproved mineral capture or industrial use. As a modelling problem this presents moving

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boundaries, crushing, unsteady flows and granular flow while the model we have chosento use introduces a variable yield stress and highly non-linear viscous term.

Chernyavsky, I., Jensen, O., Dryden, I. & Leach, L.

A Multiscale Theoretical Analysis of Flow and Transport in the Human

Placentone

The human placenta is characterised by a unique circulatory arrangement, with numer-ous villous trees hosting fetal vessels in close contact with maternal blood. The resultingmedium manifests a multiscale structure balancing microscopic delivery of nutrients andmacroscopic flow distribution. The mathematical modelling of human placental circula-tion and metabolic exchange was historically started as an application of the theory ofheat exchangers (Faber, Circ. Res. 24: 221-234, 1969). The assumptions behind theseand most of the existing models ignored both spatial uteroplacental flow distribution andplacental microarchitecture. It is therefore of interest to use the theory of flow in a porousmedium enhanced by the methods of homogenization to study placental circulation andsolute transport. The aims of this study are to examine the influence of placental structureon the effectiveness of nutrient uptake in a single placentone (the placental circulatoryunit formed by a villous tree and its corresponding maternal vessels). Our model consid-ers steady filtration of an incompressible viscous liquid in a hemispherical domain, andassumes that advective transport of solutes dominates molecular diffusion. The methodof images and computational integration along streamlines are employed to find flowand solute concentration distributions. The model indicates the existence of an optimalvolume fraction of villous tissue and shows the trade-off between overall placentone resis-tance and net solute extraction. Predictions of the model agree with radioangiographicstudies of tracer dynamics in the primate and human placentas. The work is supportedby Marie Curie EST Network MMBNOTT.

Claus, S. & Griebel, M.

Numerical Simulation of Unsteady Viscoelastic Oldroyd-B and

Phan-Thien Tanner Flows

We present a numerical scheme to compute three-dimensional unsteady viscoelastic fluidflows. Viscoelastic fluids play an important role in many industrial processes, because theflow of liquids such as molten plastics, engine oils, gels, egg white or blood is significantlyinfluenced by elasticity effects. Viscoelastic liquids show interesting and unexpected flowpatterns like rod-climbing or die-swelling, which go beyond the scope of Newtonian fluidmechanics. These phenomena are caused by the deformation of molecular chains withinthe fluid, which contributes to the stress. Hence, we require a model for the extra stresstensor for which we use the Oldroyd-B and the Phan-Thien Tanner equations. In orderto decouple the resulting equations, we employ a Chorin-type projection method. Forthe spatial discretization, we use a finite volume approach on a staggered grid, includinghigher order methods for the discretization of the convective terms. Finally, we present

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numerical results concerning the flow over a hole, a Karman vortex street and a freesurface flow down an inclined plate.

Golding, M.J. & Huppert, H.E.

The Effect of Impermeable Channel Boundaries on Gravity Currents in a

Porous Medium

The effect of impermeable channel boundaries on a gravity current propagating in aporous medium is investigated. The problem admits similarity solutions for currents of avariety of rates of input flux and channel shapes. It is found that there is a critical valueof the rate of input flux below which the current will travel faster in a narrow channel,and above which it will be faster in a channel with a flatter base. Experiments wereconducted in V-shaped and semicircular channels for gravity currents of both constantvolume and constant flux and the results are generally found to be in good agreementwith theoretical predictions.

One motivation for the study of gravity currents in a porous medium is the process ofcarbon dioxide (CO2) sequestration, whereby supercritical CO2 is pumped deep under-ground into rock saturated with salt water, which has a greater density. The CO2 risesas a buoyant plume until it reaches an impermeable boundary, at which point it spreadslaterally as a gravity current. Our knowledge of geological structure deep underground islimited to data from seismic exploration studies and bore hole data and is consequentlypoorly resolved. The theory developed in this study aims to help understand to what ex-tent the presence of more complex boundaries, namely channel boundaries, would affectpredictions for the propagation of gravity currents in porous media.

Gurney, C.J. & Decent, S.P.

Asymptotic Solution of Slender Inviscid Jet Break-Up

The break-up of a slender inviscid jet examined using the Needham-Leach asymptoicmethod. This method enables the calculation of the large time asymptotic structureof the model evolution equations using matched asymptotic expansions. We show thatin the case of an inviscid jet, large time asymptotics are more complicated than in thecase of a viscous jet, and that an inviscid solution yields more interesting dynamics thanit’s viscous counterpart. We also provide information on how the jet breaks-up and theregions of jet break-up, and yielding information on how nonlinear jets may be controlled.

Hamer, M., Graham, R. & Wattis, J.

A Combinatorial Approach to Flow-Induced Nucleation in Polymers

We analytically derive flow-induced nucleation in polymers. We use the GLaMM modelof polymer flow, in which polymer chains are divided into Z sub-chains of varying degree

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of stretch. Each sub-chain has a different nucleus attachment energy. We treat differentsub-chains as separate species and calculate the number of arrangements for a nucleusof size N containing Z distinct species. Crystallised stems run through each nucleus andeach stem must contain a single species. This produces a nucleation energy landscapefor varying N, from which the nucleation rate can be calculated. Several patterns inthe nucleation rate dependence on flow conditions are identified, which will be useful tomodels of polymer nucleation.

Hartmann, D., Meinke, M. & Schroder, W.

A Cartesian Cut-Cell Method for Compressible Viscous Flows in Complex

Geometries

In the recent years, numerical methods based on non-boundary-conforming grids to solvethe Euler and Navier-Stokes equations have gained popularity since they offer the pos-sibility to automatically generate the grid and thus allow a very efficient simulation offlows with complex embedded boundaries. One of the challenges of these methods is therepresentation of the embedded boundaries which do not coincide with grid lines.

Numerical methods which rely on a discrete representation of the embedded bound-aries without modifying the continuous governing equations can be divided into finite-difference-based methods and finite-volume based methods also referred to as Cartesiangrid or cut-cell methods. While providing discrete convergence of mass, momentum, andenergy, cut-cell methods are difficult to implement. The major obstacle towards three-dimensional implementations of cut-cell based Cartesian grid methods is the complexityinvolved in formulating a finite-volume discretization on cells which are arbitrarily inter-sected by the (embedded) boundaries of the computational domain.

In this talk a Cartesian cut-cell method for three-dimensional viscous flows is pre-sented including a general formulation to impose Dirichlet and von Neumann boundaryconditions on the arbitrarily shaped cut cells at the (embedded) boundaries of the com-putational domain. The method works on arbitrarily refined grids and allows the use ofsolution-adaptive mesh refinement. Solutions of canonical testcases such as the laminarflow past a sphere demonstrate the accuracy of the presented method.

Hoeschele, E., Wagner, B. (WIAS) & Munch, A. (Oxford)

Meniscus Coating with Hard and Elastic Contra-Rotating Rolls

The main focus of our research is the forward roll-coating process used in many industrialapplications. The understanding of the coupling between liquid flow, elastic substratedeformation and the liquid/air interface at the meniscus is essential for optimization ofthis process. The liquid properties are modeled by the full incompressible Navier-Stokesequation in the case of Newtonian liquids or a Carreau- model to treat shear thinningeffects. The elastic cover is treated as an incompressible Neo-Hookian solid. All equationsare discretized with the iso-parametric Taylor-Hood finite elements. We treat the a-prioriunknown capillary surface with arbitrary lagrangian eulerian method and a variational

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formulation for the curvature terms that arise from surface tension. Since the the shapeof deformed elastic cover is a-priori unknown, too, we write the equations on a knownreference domain with the help of the Piola transformation. The numerical schemes forthe elastic solid and the liquid are coupled via a damped Picard iteration. Using ournumerical tool, we study how the flow rate and meniscus depends on given parameterslike load force, elasticity modulus, Reynolds- and Capillary numbers.

Ismail, Z., Fitt, A. & Please, C.

A Model of Fluid Flow Through the Detached Retina

The retina is a transparent layer of sensitive tissue which is kept in contact with thechoroid (which is responsible in giving nourishment to the retina) inside the eye. Whenthe retina tear develops, it may allow liquefied vitreous humour (VH - a clear gel that fillsthe space between the lens and the retina) to flow through the retina and push the retinaaway from the choroids, thus causing a retinal detachment (RD). If the retina remainsdetached, it will lose the ability to function, vision will become distorted and finallythe patient will go permanently blind. A paradigm mathematical model of fluid flowthrough the detached retina has been developed by considering the lubrication theorylimit of the Navier-Stokes equations. In the current study fluid flow between rigid wallshas been assumed and we have considered the detached retina to be a thin flap whichit is attached to the plain wall (choroid). The detached retina is also assumed to beelastic and deformable; allowing the general theory of beam bending to be applied. Inparticular, asymptotic analysis has been used in order to calculate and analyze the flowbehaviour, the deformation of the detached retina, as well as the fluxes of fluid and thebending moment.

Iungo, G.V. & Lombardi, E.

Time-Frequency Analysis of Fluid Dynamic Signals through Proper

Orthogonal Decomposition

A procedure to perform the time-frequency analysis of fluid dynamic signals throughProper Orthogonal Decomposition (POD) is described, which may be used to characterizethe amplitude and frequency modulations of the main spectral components present inthe signals. The POD is performed using a certain number of time-portions of the givensource signal, which are denoted as snapshots and contain all the same number of samples.The time-length of the snapshots is chosen considering the frequency-resolution requiredfor the spectral analysis. The result obtained from the POD is an orthonormal basiscomprising a finite number of time-histories, denoted as POD modes, whose time-lengthis equal to that of the snapshots, and which contain the most representative fluctuationsdetectable from the source signal, sorted by their energy. The number of snapshots derivedfrom the source signal must be sufficiently high in order to associate its main spectralcomponents to different POD modes. From the spectral analysis of each POD mode themain spectral components of the source signal can then be characterized. Moreover, the

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extraction from the source signal of the spectral component represented by a POD modeis performed through an ad-hoc technique, which provides the convolution of the signalwith the considered POD mode and avoids any problem of signal amplification/dampingor phase-shift of the extracted component with respect to the source signal. The timevariations of the amplitude and frequency of each extracted spectral component are thencharacterized through the classical Hilbert demodulation technique. In order to check itsperformance, the whole procedure is first applied to computer-generated signals, and thento experimental fluid dynamic signals. Finally, the results of the procedure are comparedwith those obtained through a method for spectral component extraction based on thewavelet transform.

Kitavtsev, G., Recke, L. & Wagner, B.

Derivation, Analysis and Numerics of Reduced ODE Models Describing

Coarsening Dynamics

In this talk the topic of reduced ODE models for a set of lubrication models derivedin [1] and describing evolution of thing nanometric liquid films is addressed. Besidesformal asymptotic derivations we describe analytical and numerical investigation of suchmodels. In particular the influence of slippage on the coarsening dynamics is analyzedvia the reduced models. Some new methods for the rigorous justification of these modelsare suggested.

[1] A. Munch, B. Wagner, and T. P. Witelski, Lubrication models with small to

large slip lengths, J. Eng. Math., 53 (2006), pp. 359–383.

Klettner, C.

Tsunami Evolution

Tsunami evolution from deep water to coastal regions has been studied. In deep water,the KdV equation adequately describes how a tsunami evolves. This weakly non-linearmodel was solved numerically using a finite difference scheme and new mathematicalmeasures were established to combine deep water and near-coastal dynamics of tsunamiwaves. As the wave shoals a more complete description of the flow dynamics is needed. AnArbitrary Lagrangian Eulerian finite element method code based on the Navier-Stokesequation was developed to be able to analyse free surface phenomena. The code wasfirst written and validated with Intel Math Kernel Libraries (MKL) and parallelisedusing OpenMP. It is now being converted to run on a distributed memory architecture(with MPI as the communication protocol) with high performance libraries PETSc andMKL. Load balancing will be carried out via domain decomposition with ParMETIS. Tocomplement the computational effort experiments looking at the evolution of shoalingelevation and depression wave were carried out at Arizona State University. A novelmethod of generating depression waves was devised which allowed their changing profile

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to be recorded. Shoreline recession, a distinct feature of shoaling depression waves wascaptured in the laboratory for the first time.

Knox, D.J., Wilson, S.K., McKee, S. & Duffy, B.R.

Mathematical Modelling of the Human Knee

Bone and joint diseases pose an ever greater problem within an ageing population. It isgenerally regarded that the manufacture of artificial cartilage is the best way to tacklethis problem. However, before considering artificial cartilage it is crucial to understandthe mechanics of real cartilage which itself is deformable and porous.

Within the human knee thin cartilage layers coat the surfaces of the lateral and medialfemoral condyles and the tibial plateau, and synovial fluid acts as a lubricant in the gapbetween the two surfaces. An important issue to understand is the hydrodynamic pressureexerted on the cartilage by the lubricating fluid due to the motion of the condyles. Itwill be crucial to take this into account during the manufacturing process of artificialcartilage.

It has been proposed that the hydrodynamic lubrication is analogous to that of a journalbearing. Following the work of J.M. Skotheim and L. Mahadevan (2005) we consider anelastohydrodynamic journal bearing with the added feature of porosity.

Kopera, M.A.

Direct Numerical Simulation of Turbulent Flow over a Backward-Facing

Step

The final goal of the project is to generate hi-resolution DNS data of a high Reynoldsnumber turbulent flow over a backward-facing step for LES comparisons.

At current stage simulations are performed with Re = 6600 based on mean centrelinevelocity and step height. The flow is bounded by no-slip walls in normal direction and isassumed to be periodic in span-wise direction. Inflow is generated by recycling velocityfield from downstream part of the inflow channel. Calculations are run using Semtex CFDcode (written by H. Blackburn, Monash University, Australia) which uses hp-spectralelement method for spatial discretisation.

DNS data will be presented in comparison with previous experimental and computa-tional results.

Kwiatkowski, K. & Bajer, K.

Mixing and Reactions in the Vicinity of a Vortex

When simulating a flow in a typical industrial device we need to take into account thecoexistence of different species as well as the chemical reactions the species are engaged in.

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When the flow is non-premixed the mixing and/or diffusion can determine the wholeprocess. In a wide range of devices, the turbulence and its large coherent structures, likevortices, are generated all the time and they may have dominant effect in common regimesof operation.. There are many phenomena related to vortices, especially the accelerateddiffusion in the vortex, driven by increased gradients (Bajer, 2001). That motivates ourinterest in the influence of vortices on chemical reaction rate, depending on vortex sizeand strength (Crimaldi, 2008). We design numerical simulations to study this problemin detail.

All simulations are made using the CFD package OpenFoam. Modeling in OpenFoamis natively three-dimensional , but besides the full 3D simulation we also pay muchattention to the, simplified, 2D case where many essential ingredients of the interplaybetween advection-diffusion and chemical reactions are already present, yet not obscuredby the complexities of the 3D vortex dynamics.

Bajer, K.; Bassom, A. P. & Gilbert, A. D. (2001), Accelerated diffusion in thecentre of a vortex, J. Fluid Mech. 437, 395-411.Crimaldi, J. P.; Cadwell, J. R. & Weiss, J. B. (2008), Reaction enhancement ofisolated scalars by vortex stirring, Physics of Fluids 20(7), 073605.

Nayebossadri, S., Avital, E.J & Motallebi, F.

Flow Calculations for Human Nasal Airways and Blockage Effect on

Outflow Pattern

Computational Fluid Dynamics (CFD) calculations are carried out for steady inspirationand expiration flows in human nasal airways. It is suggested that turbulence may affectnasal resistance in inspiration for flow rates higher than 200 ml/s. Blockage put nearthe nasal valve is shown to have a significant effect on flow pattern coming out of thenostril during expiration, supporting the possibility of using external flow measurementsto detect nasal blockage.

Nicolle, A. & Eames, I.

Flow Through and Around Groups of Bodies

Many practical engineering fluid flows consist of multiple bodies which either fill most ofthe flow domain (for instance, porous media) or are grouped in localised regions. Thelatter has not been so extensively studied and is the focus of this research. To gain afundamental insight into this problem the research focused on arrays with different voidfraction φ.

The main contribution is a detailed fully-resolved two-dimensional numerical calcula-tion of the flow past large numbers of cylinders (up to N = 133) fixed in a circular array.A parallel computational code, written in a general object orientated language using latebinding and high performance numerical libraries (PETSc) was developed and run on

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UCLs supercomputer, Legion. New diagnostics were applied to understand the influenceof the array on the flow through and around the array.

An experimental apparatus was also specifically designed and build to investigate theflow field and force contributions from an array of cylinders fixed in a uniform flow. Theexperimental results provide insight into the difference between two and three-dimensionalflow patterns.

The main conclusions are that the flow past an array has three distinct regimes. Forlow φ and N , the interaction between the individual cylinders is weak. For intermediateφ, a shear layer is created and stabilised by the bleed flow through the group, resultingin a steady force on the group. For high φ, strong blocking occurs and the array acts likea solid cylinder.

Osorio-Nesme, A., Beronov, K.N. & Delgado, A.

Numerical Analysis of Heat Transfer Enhancement in Self-Sustained

Oscillatory Flows in Periodically Grooved Channels using Lattice

Boltzmann Methods

We present numerical investigation on heat transfer enhancement through time-periodicself-sustained oscillatory flows in two-dimensional channels containing either symmetric(rectangular) or non-symmetric periodic grooves for moderate Reynolds numbers Re ∼O(103) using lattice Boltzmann methods (LBM). The influence of the groove asymmetryon the flow patterns, the heat transfer and the onset of the time-periodic oscillations isstudied. For subcritical Reynolds numbers Re < Rec the flows are found stationary andthe heat transfer along the channel is mainly conducted by diffusion. It is found thatthe onset of the oscillations occurs earlier for channels with non-symmetric grooves thanthose with rectangular grooves. Results regarding convective heat transfer are presentedas a function of the driving force, in terms of the averaged Nusselt number. It is shownthat for the non-symmetric grooves, backward flows, in which the grooves of the channelact as a series of asymmetric diffusers, perform higher heat transfer than the flows flowingin the opposite direction with the grooves working as asymmetric nozzles.

Parezanovic, V. & Cadot, O.

Global Frequency Selection in a Controlled Wake

Stationary perturbation techniques are used to investigate the sensitivity of the globalproperties of the wake behind a bluff body, at moderate Reynolds numbers. The wake isproduced by a symmetric cylinder with a leading edge profiled as a semi-circle of diameterD, and a flat trailing edge, at a right angle to the flow. Its dynamics are governed by aVon Karman street global mode. Perturbation is introduced as a small, circular controlcylinder, displaced throughout the near wake, in small steps. For each position of thecontrol cylinder, we measure local velocity at 6D downstream of the primary cylinder,where the frequency of the global mode can be easily captured. These measurementsare assembled into high resolution sensitivity maps of the wake. The entire recirculation

11

bubble is found to be a sensitive region for the global frequency selection and the qualityof the synchronization. A striking position is found in its center where synchronization isdestroyed and the frequency increased. In addition, we can observe several other distinctregions, where different mechanisms are thought to be responsible for the change in globalmode frequency. High speed PIV measurements of characteristic positions of the controlcylinder shed some light on the underlaying mechanisms, which are interpreted in termsof vorticity interaction, flow reattachment and flow deviation, each being dominant in acertain region of the flow.

Prignitz, R. & Bansch, E.

Particulate Flows

A method is presented for the simulation of viscous incompressible flow with many sus-pended solid particles. This method uses a finite-element discretisation in space and anoperator-splitting technique for discretisation in time and has its basis in work by Glowin-ski et al.. However, a subspace projection rather than a Lagrange multiplier is used tocouple the particle motion with the fluid motion. Combined with local mesh refinementthe method results in a fast and accurate algorithm for the simulation of a huge numberof particles in a flow field. Validation is achieved using the sedimentation of one particleand comparing the resulting drag coefficient with theoretical and experimental results.

Remmler, S., Christophe, J. & Anthoine, J.

Computation of the Trailing-Edge Noise of an Airfoil Based on Steady

Flow Data

The broadband noise emitted from the interaction between the trailing-edge of an airfoiland its boundary layer was computed based on a steady Reynolds-averaged Navier-Stokessolution of the flow field. Therefore the pressure spectrum on the airfoil surface near thetrailing-edge was calculated from the mean velocity and the turbulent kinetic energydata. The obtained information were used to compute the radiated sound by means ofAmiet’s theory of airfoil sound. Both, wall pressure and radiated sound spectra, werecompared to experimental results for validation. The computations were made on thecase of a Valeo Controlled Diffusion (CD) airfoil placed in jet in the anechoic facility ofcole Centrale de Lyon. For this case wind tunnel measurements as well as large eddysimulation results were available.

Samad, A. & Garrett, S.

Absolute Instability of the Boundary Layer due to Rotating Prolate

Spheroids

Although its precise role in the transition mechanisms is still to be clarified, local absoluteinstability is known to exist in the boundary-layer flows over rotating disks, cones and

12

spheres. We extend these analyses to the family of prolate spheroids rotating in otherwisestill fluid. Each spheroid is characterised by an eccentricity parameter, e, and the resultingperturbation equations reduce to those for the sphere for e=0. The effect of e on the localabsolute instability at different latitudes will be discussed in detail.

Setchi, A., Siggers, J., Mestel, J. & Parker, K.

Mathematical Model of Flow through the Ductus Arteriosus

The ductus arteriosus is the vascular connection between the pulmonary artery and theaortic arch in the developing foetus. It normally closes within 48 hours after birth. Failurefor this to happen results in a condition called patent ductus arteriosus (PDA). It is vitalto diagnose the defect early, know the side effects and predict its development. Modellingthe local behaviour of the flow near the ductus arteriosus is important as informationabout the mixing properties (between oxygenated and non-oxygenated blood) and thelocal pressures and stresses can be crucial in determining the impact of its patency.However, due to the difficult geometry associated with the shunt, there are no developedmodels that study flow through it locally.

Sprittles, J.E. & Shikhmurzaev, Y.D.

Flow Over Chemically Patterned Surfaces

The classical fluid dynamics boundary condition of no slip suggests that variation inthe wettability of a solid should not affect the flow of an adjacent liquid. However,experiments and molecular dynamics simulations indicate that this is not the case. Inthis presentation I will show how flow over a solid substrate with variations of wettabilitycan be described in a continuum framework using the interface formation theory. Resultsdemonstrate that a shear flow over a perfectly flat solid surface is disturbed by a changein its wettability, i.e., by a change in the chemistry of the solid substrate. This work isextended to consider the case of an intermittently patterned surface.

Stewart, P., Waters, S. (Oxford), Billingham, J. & Jensen, O.

Local and Global Instabilities of Flow in a Flexible-Walled Channel

We consider the motion of high-Reynolds-number flow through a long finite-length planarchannel, where a segment of one wall is replaced by a membrane held under longitudinaltension. The flow is driven by a fixed pressure difference across the full length of thechannel. We consider the local linear stability of the uniform base state in each ofthe three compartments, identifying the hydrodynamic and surface-based modes thatpropagate in the system and describe the large-Reynolds-number asymptotic structure oftheir eigenfunctions. Furthermore, we show how these local modes combine to generate amode-1 global instability about the uniform base state; the corresponding neutral stability

13

curve (in parameter space spanned by Reynolds number and dimensionless membranetension) agrees well with fully non-linear finite-element simulations.

Tee, B.T., Li, L.K.B. & Nickels, T.B.

Experimental Study of Turbulent Boundary Layers over Smooth Surface

and a Single 2D Roughness Element

Recent research of turbulent boundary layers over roughness element has focused onunderstanding and characterizing their structure by using various advanced experimentaland numerical techniques. This work presents the measurement of a fully-developedzero pressure gradient turbulent boundary layer interacting with a single 2D roughnesselement. Mean velocity profiles were measured using 2D PIV over a smooth surfaceand a single roughness element which was a perspex rod with diameter of 5 mm and alength of 0.9 m. The experiments were conducted at Reynolds numbers (based on themomentum thickness) ranging from 3290 to 4650. Three types of outer velocity scales:friction velocity, freestream velocity and mixed outer scales were applied to analyze thevelocity defect profiles for both cases.

Tettamanti, F.A. & Mestel, A.J.

Flow through Toroidal Pipes of Small Curvature

Since its first formal study by Dean (1928), various methods have been employed to modelfully developed flows through toroidal pipes. These techniques have proposed conflictingtheories regarding the characteristic flow at high Dean’s number (K); not least of whichis the asymptotic behaviour of the friction ratio and the bifurcation from a two-vortex toa four-vortex structure. Following the work of Dean and, more recently, Van Dyke, weconsider a series solution in K for the stream function (Dean’s Series). Using the algebraicprogramming language MAPLE, we are able to extend Dean’s series up to the K32 term.In accordance with Van Dyke’s analysis, the radius of convergence is limited by a square-root singularity of K, in the complex plane. By calculating this singularity with higherprecision, we are able to estimate the value of a second singularity, the analysis of whichwill provide a better understanding of the flow at large values of K, whose asymptoticstructure is still not fully understood.

In addition, we investigate an alternative Pade Approximant technique, introduced byTourigny and Drazin, in order to identify and construct the two solution branches foundby other techniques.

14

Thompson, A., Billingham, J., & Tew, R.

Surface Tension Driven Flow in a Half Plane

We study the motion of a fat wedge of inviscid fluid, of angle π− ǫ with ǫ ≪ 1, in contactwith a rigid wall along one edge. Initially the fluid is at rest. When t = 0, the contactangle at the tip of the wedge is changed to π − λǫ. The resulting flow and motion of thecontact point are determined by a balance of surface tension and inertia. As there are nogeometric lengthscales imposed, we obtain a similarity solution with lengths scalings ast2/3. When λ = O(1), we can linearise the domain to a half plane, with the free surfacedisplacement coupled to the velocity potential via linear boundary conditions. We solvethe leading order BVP numerically, with the aid of the boundary integral method, andalso present asymptotic solutions for λ ≫ 1 and |λ − 1| ≪ 1. For λ ≫ 1, the asymptoticsolution can be constructed in terms of an inner and an outer region, with the phase andamplitude of the capillary wave on the free surface set in the inner region via the solutionto the dock problem. The decay of the mean free surface displacement matches into theouter region to determine the relationship between λ and the contact point position xc.For |λ−1| ≪ 1, the leading order problem can be solved exactly using Mellin transforms.

Vancea, I., Thiele, U., Stannard, A., Pauliac-Vaujour, E., Martin, C.P.,Blunt, M. & Moriarty, P.J.

Branching Patterns in Evaporative Dewetting: A Kinetic Monte Carlo

Approach

A kinetic Monte Carlo model [Rabani et al, Nature 426, 271 (2003)] has been employed,which allows to study the influence of the nanoparticles on the basic dewetting behavior,(on spinodal dewetting and also on dewetting by nucleation and growth of holes) and aswell to study how nanoparticles strongly destabilize straight or circular dewetting frontsin the nucleation regime. The main work has entirely focused on a numerical study oftransversal front instability.

After introducing the model and the motivation to use it we are analyzing the depen-dence of major parameters, like effective chemical potential, mobility of the nanoparticles,and their concentration, on branching patterns. We have also investigated the dependenceof the fingering on the interaction strengths (the influence of the energetics of the system).

Veremieiev, S., Thompson, H.M., Lee, Y.C. & Gaskell, P.H.

Modelling Inertial Thin Film Flow over Substrate with Topography

The deposition and flow of continuous thin liquid films over man-made or naturally oc-curring functional substrates containing regions of micro-scale topography is of greatimportance in numerous engineering and biologically related fields. For example, in thecontext of engineering processes thin film flows play a key role in photo-lithography andthe laying down of precision coatings, while in biological systems they play a role in areas

15

as diverse as tissue engineering and plant disease control. In this work, gravity-driventhin film flow over substrates containing topography is explored using a novel approachinvolving the derivation and efficient Full Multigrid solution of a depth-averaged non-linear form of governing unsteady Navier-Stokes equations. The key advantage of thisapproach is that it enables the latter to be reduced to a more tractable coupled systemof partial differential equations that, in contrast to the commonly used lubrication equa-tions, enables the influence of inertia to be accounted for. Several problems involvingone- (spanwise) and two-dimensional (localised) topographical features are explored andresults compared (where possible) with complementary experimental data and finite el-ement solutions of the full Navier-Stokes problem; the latter enabling the influence ofinertia to be quantified. In addition, the prospect of using a static electric field as ameans of control the associated gross free-surface disturbance is investigated. It is shownthat an electric field can be used to suppress the capillary ridges and depressions whichform, thus leading to improvement in the planarity of the free-surface.

16

Posters

Ahmad, A., Cater, J., Avital, E., & Lawn, C.

Experimental Aeroacoustics Study on Jet Noise Reduction using

Tangential Air Injection

Aircraft jet exhausts are a source of undesirable noise and continue to be an area ofinvestigation driven by increasingly stringent regulation. The noise is produced by theunsteady mixing of the jet with the surrounding air and is dominated by the effects ofthe shear layer. In this study, unheated jets of Mach 1.3 are used to achieve the sameconvective Mach number commonly found in civil aircraft jet exhausts and measurementsare taken to explore the effects of a tangential flow component generated through twodistinct injection methods. The first technique consists of tangential flow injectors locatedupstream of the nozzle exit whereas the second involves an equal number of control jetsspaced further downstream around the nozzle exit. Acoustic measurements were madein an anechoic chamber equipped with an array of 10 free-field microphones whilst localflow field conditions were observed using Particle Image Velocimetry (PIV). Althoughboth forms of tangential injection allowed for reductions in sound pressure levels (SPL)at a range of observer angles, external injection was found to be more efficient throughachieving similar noise reductions at only a fraction of the injection mass flow ratio. Themost significant example was at the sideline angle noise spectra which shows an 18dBreduction that totally eliminated both broadband shock and screech noise at a Strouhalnumber of 0.75, however at the expense of increased high frequency noise beyond St=2.Current research is aimed at investigating an effectively mass-less synthetic jet injectionsystem for noise reduction. The ultimate objective is to develop a configuration thatrequires minimal air injection for maximum noise reduction whilst minimising weightand thrust penalties.

Augier, P., Billant, P., Negretti, E. & Chomaz, J.M.

Experimental Study of Forced Stratified Turbulence

Recent results show that strongly stratified turbulence has a three dimensional dynamicinstead of a quasi-two dimensional dynamic conjectured previously. A direct cascadeassociated with a k−5/3 horizontal kinetic energy spectrum has been predicted when thebuoyancy Reynolds number is sufficiently large [Lindborg, 2006].

In order to check this hypothesis, we investigate experimentally forced stratified tur-bulence. The flow is generated by 12 vortex generators (flaps) placed on the side of alarge stratified tank. Each generator produces periodically and independently a counter-rotating vertical columnar vortex pair which propagates toward the central part of thetank. The interaction of the randomly produced vortex pairs give rise to a statisticallystationary turbulent flow with a low Froude number and a buoyancy Reynolds numberof order unity.

17

PIV measurements in vertical cross-sections show that the flow organises itself intohorizontal layers via the zigzag instability. Horizontal velocity spectra obtained by PIVmeasurements in horizontal cross-sections exhibits a narrow inertial domain in agreementwith the DNS of forced stratified turbulence performed by Brethouwer [2007] for buoyancyReynolds number larger than unity.

Fay, G. & Fowler, A.

Modelling Geophysical Hazards

A number of geophysical hazards that threaten populations, land and infrastructure canbe modelling as granular fluids. These include pyroclastic flows, snow avalanches, turbid-ity currents and debris flows. Many theories have been suggested as a means of modellingthese hazards and, as yet, there is no fully accepted mathematical approach.

The 3- and 4-equation Parker model presented by Parker, Fukushima and Pantin in theJournal of Fluid Mechanics in 1986 provides one means of modelling granular geophysicalhazards. It has been applied to study of turbidity currents and snow avalanches and Ihope to consider the applicability of the Parker model to both pyroclastic flows and debrisflows.

Iungo, G.V. & Buresti, G.

Experimental Investigation on the Aerodynamic Loads and Wake Flow

Features of a Low Aspect-Ratio Circular Cylinder

An experimental investigation is described which was carried out in order to characterizethe flow features of the wake generated from a circular cylinder with aspect ratio 3and placed vertically on a plane. Force measurements were performed using a strain-gage balance at Reynolds numbers ranging in the interval 6 × 104 ≤ Re ≤ 1.1 × 105.The mean drag coefficient, CD, is found to be roughly invariant by varying the testedReynolds numbers and a mean value CD = 0.81 is found. As for the fluctuating forces,a dominant spectral component could clearly be detected in the wavelet spectra only forthe signals of the cross-flow force, with an average Strouhal number of 0.156. A spectralcontribution with roughly the same Strouhal number is detected from velocity signalsacquired, through a hot-wire single-component probe, in proximity to the lateral wakeboundary, and its energy is found to decrease by moving the probe away from the wakeand upwards. Simultaneous measurements carried out at symmetrical locations withrespect to the wake symmetry plane, and analysed through a time-frequency techniquefor component extraction and cross-correlation analysis based on the wavelet and Hilberttransforms, showed that these fluctuations can confidently be ascribed to an alternatevortex shedding. Subsequently, dynamic measurements of the pressure field over thelateral surface and the free-end of the model were carried out. From these measurementsthe spectral component connected to vortex shedding is found over the lateral surface,with maximum energy at an azimuthal position just before the separation of the shearlayers. The fluctuating energy connected to vortex shedding decreases by moving towards

18

regions immersed in the separated wake, and with increasing vertical coordinate; as amatter of fact, above about 50% of the model height an evident energy peak cannot bedetected anymore. This feature highlights that a regular alternate vortex shedding occursonly for the lower half-span of the model and that the remaining part is dominated by theupwash generated by the flow passing over the free-end. From the spectral analysis of thepressure measurements carried out over the model free-end no evidence of the presenceof the spectral component at St = 0.15 is found, as expected. However, a significantfluctuating energy is observed at lower dominating frequencies.

Joda, A., Fisher, J., Korossis, S. & Jin, Z.

Fluid-Structure Interaction of Mechanical and Tissue Heart Valves

A numerical simulation that closely represents the physiological behavior of native heartvalves, including the motion of the leaflets and the dilation of the aortic root, requiresthe incorporation of the fluid flow through the valve and valve structures deformation.Fluid flow affects the opening and closing behavior of the valve and vice versa. Couplingcomputational fluid dynamics and structural analysis is called fluid-structure interaction(FSI). The aim of this work was to develop and validate a coupled 3D FSI model of heartvalves using a finite element software. The developed methodology can provide importantinformation regarding fluid dynamics and stress-strain distribution in heart valves, whichcan be used to design and develop new artificial and tissue engineered heart valves.

Kitavtsev, G., Recke, L. & Wagner, B.

Derivation, Analysis and Numerics of Reduced ODE Models Describing

Coarsening Dynamics

In this poster the topic of reduced ODE models for a set of lubrication models derivedin [1] and describing evolution of thing nanometric liquid films is addressed. Besidesformal asymptotic derivations we describe analytical and numerical investigation of suchmodels. In particular the influence of slippage on the coarsening dynamics is analyzedvia the reduced models. Some new methods for the rigorous justification of these modelsare suggested.[1] A. Munch, B. Wagner, and T. P. Witelski, Lubrication models with small to

large slip lengths, J. Eng. Math., 53 (2006), pp. 359–383.

Krasnopolsky, B.I.

Numerical Investigation of Flow Stability and Heat Transfer past an Open

Cubic Cavity

The problem of three-dimensional flow over cavities is of interest for a wide range of scien-tific and engineering applications, for example, in the automotive and aircraft industries,

19

in ecological problems, in civil engineering, and in many other fields. We consider flowover the cavity with laminar boundary layer at the inlet. Such flow is described by thesystem of Navier-Stokes, continuity and energy equations in the Boussinesq approxima-tion with corresponding boundary conditions. Our aim is to investigate the influence ofsystem parameters and inlet boundary layer perturbations on the heat transfer intensifica-tion from the bottom of the cavity. To solve this problem we have developed a numericalalgorithm for rectangular cavities at staggered grids. The calculations show that param-eters of the incoming boundary layer play an important role in the flow stability andheat transfer in cavities. For example, the perturbation frequency of the boundary layerat the inlet does not influence the flow stability in the cavity for thick boundary layers;however, for thin inlet boundary layers some perturbation frequencies lead to periodicflow or non-periodic turbulent regime. We demonstrate that flow in the cavity and heattransfer from the bottom of the cavity depend directly on the stability of a shear layerbetween the cavity and the main stream; the perturbation frequencies of the boundarylayer at the inlet, corresponding to the heat transfer intensification, are in a good agree-ment with the frequencies corresponding to the maximum growth rates of perturbationsin the shear layer in terms of linear stability analysis.

Kumar, D. & Sreenivas, K.R.

Numerical Simulation and Experimental Investigation of Salt Diapirs

Salt diapers are dome shaped geological structures formed by intrusion of evaporativemineral-deposits rising through, sediment of soil bed. The characteristic length scale ofthese structures is the diameter ( 1000m) and the spacing between them ( 10km) andrising-velocity is another important factor. In this paper we study the dependence ofthese factors on governing parameters like ratio between heights of mineral dopiest andover laying sedimentary layer, viscosity and the density difference between these two lay-ers. In nature, because of very high viscosity, the emplacement of salt layer into soil-layerhappens over geological time scales. In this work, we present results from 2-D numericalsimulations and laboratory model experiments to elucidate characteristics of salt-diapirsand its dependence on governing parameters. We in this study considered a two-layersystem that contains heavier layer fluid lying over lighter fluid layer and these layers areof different thickness. For simulating this system, a code based on finite volume dis-cretization and semi implicit method for pressure linked equations revised (SIMPLER)algorithm is used. Boundary conditions used are no-slip & impermeable condition forvelocities on the walls, with no mass transfer across the system boundaries. Initial con-dition is a step-profile for concentration (density) with heavier fluid (sedimentary soillayer) laying-over lighter fluid layer (evaporative mineral layer) and is allowed to evolvein time due to diffusion and convection. Resulting Rayleigh-Taylor fluid instability helpsin understanding characteristics of salt-diapirs on various governing parameters. We havealso done experiments with similar configuration in a box in with an initial step change indensity across an interface (stable) using two layers of fluids with different densities andhigh viscosities. We used CMC (Carboxy Methyl Cellulose) to vary the viscosity of thewater and sugar to increase the density. The unstable density stratification was obtained

20

by inverting (rotating by 180o) the box. Experiments are done with different density dif-ference and layer thickness ratios. Experimental results provide qualitative verificationof the simulations. The effect of these parameters on diapirs spacing and shape will beexplained in the final presentation.

Orazzo, A., Coppola, G. & de Luca, L.

Transient Growth in Core-Annular Flow

The classical problem of the stability of Core-Annular Flow (CAF) in pipes is here re-considered from the point of view of linear non modal analysis. An accurate Chebyshevpseudospectral code in polar coordinates has been developed in order to separately dis-cretize the two phases of the flow. The classical tools of non modal analysis (namelypseudospectra, growth function and optimal perturbations) have been employed in orderto assess the effects of non normality on transient evolution of small perturbations tocore-annular base flow. Linear transient growth of three dimensional perturbations iscomputed for typical potentially stable configurations, by taking into account the effectsof viscosity and volume ratios between the two liquids, as well as of Reynolds numberand surface tension. A detailed numerical investigation has been conducted on wide re-gions of the parameters space and the occurrence of substantial transient growth has beenfound for asymptotical stable configurations. Optimal perturbations for the most criticalparameters have been determined and their structure during the unsteady evolution hasbeen considered. It is found that in situations in which axisymmetric modes of distur-bance are expected to constitute the most dangerous ones, in subcritical conditions spiraldisturbances can provide higher levels of energy amplification.

Tiong, W.K.

Propagation of a Solitary Wave and Undular Bore over a Slope

The Korteweg-de Vries (KdV) equation is widely known as a universal equation to de-scribe the weakly nonlinear waves in many branches of physics and engineering. Sincethen, there have been many interests in propagation of nonlinear dispersive waves suchas a solitary wave over variable depth. The propagation of nonlinear dispersive waves insuch problems is described by the KdV equation with variable coefficients (Grimshaw,1970; Johnson, 1973). This equation is solved using the method of lines with finite dif-ference approximations for the space derivatives and fourth-order Runge-Kutta schemefor the time integration. Some numerical solutions of propagation of a solitary waveand undular bore over a slope in the framework of variable-coefficient KdV equation arepresented here.

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