Theme
Organizers: Ian Frigaard (UBC), Richard Karsten (Acadia) and Bartosz
Protas (McMaster)
This
theme will coincide with the 20th Canadian Symposium on Fluid
Dynamics (CSFD2012). This Symposium is a biannual event bringing
together researchers interested in the theoretical and computational
aspects of fluid dynamics as well as in applications. Symposium
topics
will include, but are not limited to, turbulence, geophysical flows,
multiphase and complex flows, mathematical and computational methods,
aerodynamics.
Confirmed
Speakers
Tahmina
Akhter,Ryerson
Dave Amundsen, Carleton
Youssef Belhamadia, Alberta
Yves Bourgault UOttawa
Lydia Bourouiba,MIT
John Bowman , UofA
Robert Bridson, UBC
Walter Craig, McMaster
Hans De Sterck, Waterloo
Colin Denniston,UWO
Matthew Emmett, University of North Carolina
Mohammad Farazmand,McGill
Razvan Fetecau (Yanghong Huang), SFU
Jan Feys, McGill
J.M.Floryan, UWO
Ian Frigaard, UBC
Alex Hay, Dalhousie
Tiger Jeans, UNB
Sarah Hormozi, UBC
Hossein Amini Kafiabad, McGill
P.N.Kaloni, Windsor
Ida Karimfazli,UBC
Richard Karsten, Acadia
Brendan Keith, McGill
Boualem Khouider, UVic
Mary Catherine Kropinski, SFU
Michael Lindstrom
Frances
Mackay, Western
Peter
Minev, UofAlberta
James Munroe, Memorial
Lidia Nikitina, Carleton University,
Mohammad Niknami,Western
Robert Owens, Universite de Montreal
Dominique Pelletier, Ecole Polytechnique
Montreal
Nicolas Perinet, UOIT
Francis Poulin, Waterloo
Bartosz Protas, McMaster
Bryan Quaife, University of Texas
A. Roustaei, UBC
Amir Sayed, Carleton University
Samuel Shen, San Diego State University
Ray Spiteri, U Saskatchewan
Marek Stastna,Waterloo
Catherine Sulem UofT
YuHau Tseng, York University
José Urquiza,Laval
Henry van Roessel, UAlberta
Lennaert van Veen, UOIT
Mike Waite, Waterloo
Jonathan Wylie, City University of Hong Kong
Xiaohua Wu, Royal Military College
David Zingg, UTIAS, UofT

POSTDOCS
Maurizio Ceseri, SFU (John Stockie)
Harish Dixit, UBC (Bud Homsy)
Nicolas Perinet, UOIT (Greg Lewis)
Driss Yakoubi (U Laval, José Urquiza)

Malcolm Roberts (UofA, John Bowman)cancelled
Jahrul
Alam (Memorial)
Iakov Afanassiev (Memorial)
Lucy Campbell (Carleton)
Entcho Demirov (Memorial)
Yvan Maciel (Laval)
Abstracts
Tahmina
Akhter, Ryerson University
Role of Compressibility and Slip in Blood flow through a Stenosis
One
type of blood disease is the narrowing of a blood vessel known
as stenosis, and high cholesterol is one of the main causes for
this. Suitable mathematical models are important to describe the
resulting effect on blood flow, and to study the problem analytically,
as well as numerically. An approximate analytical solution for
compressible flow through a stenosis will be presented and compared
to a numerical solution obtained using a particlebased method
called Multiparticle Collision Dynamics (MPC). Results will be
shown for various degrees of severity of the constriction, various
Reynolds numbers, and slip as well as noslip boundary conditions.
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David Amundsen, Carleton University
Resonant
Response in Acoustic Wave Systems
Coauthors: M. Mortell (UC Cork), B. Seymour (UBC), T. Shatnawi (Carleton)
The
response of acoustic wave systems under resonant, or nearresonant,
forcing is well studied and has implications for a range of industrial
applications. Classically such problems are associated with shocked
profiles which rapidly manifest even under weak forcing. Recent
studies have shown, however, that when features such as geometry
or underlying density stratification are varied, the shocks may
be eliminated and continuous resonant solutions arise. The nature
of the transition between these two regimes is not well understood.
Through consideration of a particular class of simple, axisymmetric
geometries I will present some preliminary results and insights
into the connection between these two qualitatively distinct outcomes.

Youssef
Belhamadia, Universisty of Alberta
Numerical Modeling of Phase Change Problems with Convection
Coauthors: Abdoulaye Kane and André Fortin
Phase
change problems with natural convection play a significant role
in several industrial applications. The main challenge is to accurately
compute the liquidsolid interface where phase change occurs.
This phase change boundary is time dependent and its morphology
can be affected with the melt flow. In this work, an enhanced
formulation based on the enthalpyporosity method is proposed
where the different thermophysical properties between the two
phases can be easily taken into account. Accurate temporal and
spatial discretizations are also employed for solving the proposed
formulation. Numerical simulations are presented and compared
to the experimental data to illustrate the performance of the
proposed methodology.

Yves
Bourgault (University of Ottawa)
Domain Decomposition Methods for Modelling Mass Transfer in Fuel
Cells
Coauthors: Hamidreza Khakdaman and Marten Ternan, University of
Ottawa
Mathematical
models of mass and charge transfer in fuel cells give rise to
a system of nonlinear partial differential equations (PDE). These
PDE must be solved over subdomains representing the anode, electrolyte
(membrane) and cathode using coupling transfer boundary conditions.
The implementation of the usual transfer boundary conditions within
a Schwarz domain decomposition method with finite element discretization
did not turn out to be effective. We are proposing as an alternative
to use NeumannNeumann coupling boundary conditions at the membrane/electrode
interface. Special care is required for proton conservation as
Neumann boundary condition are needed on all exterior boundaries
and the ground state of the electrolyte potential must be properly
set to ensure an equal total reaction on the anode and cathode
subdomains. The numerical strategy adopted and numerical results
will be presented.
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(c)Lydia
Bourouiba, Massachusetts Institute of Technology
Energy transfers in rotating turbulence
Turbulent
flows subject to solidbody rotation are known to generate steep
energy spectra when twodimensional columnar vortices dominate.
The dominant mechanisms leading to the accumulation of energy
in the twodimensional columnar vortices remain undetermined.
Here, I will discuss the discreetness effects that could arise
and affect the energy transfers in rotating flows when examined
in finite and periodic domains and discuss the scalelocality
of the nonlinear interactions directly contributing to the growth
of the twodimensional vortices. Implications for existing theories
of rotating flows will be discussed.
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John
Bowman, University of Alberta
Coauthors: Malcolm Roberts
Pseudospectral Reduction of Incompressible TwoDimensional
Turbulence
The
turbulence decimation technique known as spectral reduction was
originally formulated entirely in the wavenumber domain as a coarsegrained
wavenumber convolution in which bins of modes interact with enhanced
coupling coefficients. A Liouville theorem leads to inviscid equipartition
solutions when each bin contains the same number of modes. A pseudospectral
implementation of spectral reduction which enjoys the efficiency
of the fast Fourier transform is described. The model compares
well with full pseudospectral simulations of the twodimensional
forceddissipative energy and enstrophy cascades.
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Robert Bridson, UBC Computer Science
Coauthors: Tyson Brochu (UBC) Christopher Batty (Columbia) Todd
Keeler (UBC) Essex Edwards (UBC)Surface Tracking, Triangle Meshes,
and Fluids in Movies
We consider recent developments in our dynamic triangle mesh front
tracking method, as embodied in the El Topo software. Our general
approach to avoiding the trickiest potential mesh tangling scenarios
is to never allow the mesh to selfintersect, resolving motioninduced
intersections with contact handling algorithms adopted from solid
mechanics in the worst case. This lets us efficiently track extremely
thin and extremely complex volumes efficiently and robustly. We
highlight its application to incompressible flow for visual effects
in film, particularly free surface water (where topology change
is one of the biggest challenges), as well as smoke and fire (where
standard methods run into systems problems in film production).
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Walter Craig, McMaster University
On the dimension of the Navier  Stokes singular set
In
the hypothetical situation in which a solution u(t, x) of the
NavierStokes equations in three dimensions develops a singularity
at some singular time t = T, it could do this by a failure of
regularity, or more seriously, it could also lose energy through
concentration. The famous Caffarelli Kohn Nirenberg theorem on
partial regularity of weak solutions gives an upper bound on the
Hausdorff dimension of the singular set S(T). I will describe
a microlocal lower bound on the singular set, given in terms of
local properties of the Fourier transform of the solution. The
first result is that, if the singular set is nonempty, then there
is a lower bound on the dimension of the wave front set WF(u(T,
.)) associated with the singular set S(T), namely, singularities
can only occur on subsets of phase space T*(R^3) which are sufficiently
large. Furthermore, energy concentration at time T implies that
the solution is discontinuous in L^2, for which we identify a
closed subset S'(T) of the singular set S(T) on which the L^2
norm concentrates at time T. We then give a lower bound on the
microlocal manifestation of this L^2 concentration set, which
is larger than the general one above. An element of the proof
of these two bounds is a novel global estimate on weak solutions
of the NavierStokes equations which have sufficiently smooth
initial data.

Hans De Sterck ,
University of Waterloo
Coauthors: Lucian Ivan, Scott Northrup, Clinton Groth
Hyperbolic Conservation Laws on 3D CubedSphere Grids: A
Parallel HighOrder SolutionAdaptive Simulation Framework
A
scalable cubedsphere grid framework is described for 3D fluid
flow simulations in domains between two concentric spheres. Our
first main contribution compared to existing cubedsphere codes
is the design of a genuine multiblock implementation, leading
to flux calculations, adaptivity, implicit solves and parallelism
that are fully transparent to the boundaries between the six cubedsphere
grid sectors. This results in the first fully adaptive threedimensional
cubedsphere grid framework, with excellent parallel scalability
on thousands of compute cores. Our second main contribution is
a highorder finitevolume method that is naturally uniformly
highorder on the whole cubedsphere grid including at sector
boundaries. Cubedsphere grids are gaining increasing prominence
in a variety of application fields, including weather and climate
simulation and astrophysics, and our work is at the leading edge
of these developments in terms of parallel 3D adaptivity and highorder
capabilities.
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Colin
Denniston, University of Western Ontario
Coauthors: Frances MacKay, Santtu Ollila
Modelling Porous Colloidal Systems of Particles in a Compressible
Fluid
We
discuss the implementation of hydrodynamics interactions of colloidal
particles through a compressible, thermally fluctuating fluid.
We discuss issues related to ensuring the colloids react dynamically
so that they have a well defined mass in immersed boundary types
of simulations. Examples, such as shear melting of colloidal crystals
and hydrodynamic entrainment of particles in a channel are used
to illustrate the models.
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Matthew Emmett
University of North Carolina
Coauthors: T.B. Moodie
Formation of bed ripples due to the passage through the critical
Froude number of dambreak flows
When
a semiinfinite body of homogeneous fluid initially at rest behind
a vertical retaining wall is suddenly released by the removal
of the barrier the resulting flow over a horizontal or sloping
bed is referred to as a dambreak flow. When the bed is no longer
stable so that solid particles may be exchanged between the bed
and the fluid the dynamics of the flow become highly complex as
the buoyancy forces vary in space and time according to the competing
rates of erosion and deposition. Furthermore, when the Froude
number of the flow is close to unity perturbations in the height
and velocity profiles grow into Nwaves and the bed below develops
ripples which act to sustain the Nwaves in the fluid above. It
is our intention here to study dambreak flows over sloping erodible
beds and the development of bed ripples.
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(C)
Mohammad Farazmand, Department of Mathematics and Statistics,
McGill University
Coauthors: George Haller, Department of Mechanical Engineering &
Department of Mathematics and Statistics, McGill University
Locating coherent structures in turbulent flows using the
geodesic theory of transport barriers
We
use the recently developed geodesic theory of transport barriers
[Haller & BeronVera, submitted to Physica D (2012)] to locate
a variety of Lagrangian Coherent Structures (LCSs) in twodimensional
turbulent flows. We review the numerical challenges in the implementation
of the theory, and describe a numerical algorithm that addresses
these challenges. The algorithm is in turn illustrated on direct
numerical simulations of decaying and forced Navier–Stokes
turbulence. In particular, we identify
hyperbolic barriers (generalized stable and unstable manifolds)
and elliptic barriers (Lagrangian
vortex boundaries) in the flow. The latter barriers enclose coherent
vortices that are more robust and live longer than typical vortices
in turbulence. We also identify a systematic difference in the
size of Lagrangian eddies in forced and decaying turbulence.
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Yanghong Huang, Simon
Fraser University
Coauthors: Y. Huang T. Kolokolnikov, Razvan Fetecau
Swarm dynamics and equilibria for a nonlocal aggregation model
We
consider the aggregation equation rt?·(r?K*r) = 0 in Rn,
where the interaction potential K models shortrange repulsion
and longrange attraction. We study a family of interaction potentials
with repulsion given by a Newtonian potential and attraction in
the form of a power law. We show global wellposedness of solutions
and investigate analytically and numerically the equilibria and
their global stability. The equilibria have biologically relevant
features, such as finite densities and compact support with sharp
boundaries.
(C)Razvan
C. Fetecau, Simon Fraser University
Coauthors: Joint work with Angela Guo, Simon Fraser University.
A mathematical model for flight guidance in honeybee swarms
When
a colony of honeybees relocates to a new nest site, less than
5of the bees (the scout bees) know the location of the new nest.
Nevertheless, the small minority of informed bees manages to provide
guidance to the rest and the entire swarm is able to fly to the
new nest intact. The streaker bee hypothesis, one of the several
theories proposed to explain the guidance mechanism in bee swarms,
seems to be supported by recent experimental observations. Originally
proposed by Lindauer in 1955, the theory suggests that the informed
bees make highspeed flights through the swarm in the direction
of the new nest, hence conspicuously pointing to the desired direction
of travel. Once they reach the front of the swarm, they return
at low speeds to the back, by flying along the edges of the swarm,
where they are less visible to the rest of the bees. This work
presents a mathematical model of flight guidance in bee swarms
based on the streaker bee hypothesis. Numerical experiments, parameter
studies and comparison with experimental data will be presented.
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Jan Feys, McGill University
Coauthors: Sherwin A. Maslowe
Stability of a Trailing Vortex
A
similarity solution for an aircraft trailing vortex, valid far
downstream of the wingtip, was found by Batchelor (1964). Its
stability has been the focus of many papers, beginning with Lessen
et al. (1974). Motivated by the recent experiments of Lee &
Pereira (2010), we consider a family of profiles discovered by
Moore & Saffman (1973) that better describes the axial flow
deficit observed near the core of the vortex. In this talk, we
present results for the latter profiles and compare the growth
rates with those for the Batchelor vortex.
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J.M.
Floryan
Dept. of Mechanical and M aterials Engineering, The University of
Western Ontario
Direct Determination of Control Actuation
Changing/modifying
state of a flow requires an external input, which we shall refer
to as control actuation. Actuation can be introduced either at
the boundary of fluid domain or throughout the fluid volume. The
magnitude and distribution of actuation determine the form of
the new state. Knowing the desired state, it is advantageous to
determine the required actuation directly. Unfortunately, this
cannot be done as, typically, flow problem specification requires
specification of the actuation first to be followed by determination
of the corresponding state. Actuation that produces the desired
form of the flow is found iteratively and thus is computationally
costly. Many examples of iterative algorithms can be found in
the literature. The intent of this work is to demonstrate that
a direct determination of the actuation is possible, i.e., we
specify the desired flow property and determine the required actuation
directly.
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Ian
A. Frigaard, University of British Columbia
Coauthors: Kamran Alba, Seyed Mohammad Taghavi
A Weighted Residual Method for 2Layer Flows with Yield Stress
Fluids
Buoyancy
dominated displacement flows are important in many industrial
processes. In operations such as oilfield cementing, fracturing
and drilling the fluids involved are nonNewtonian. An industrially
relevant regime is that in which weak inertial effects are present.
Density differences often lead to stratification during displacement
and potentially to instability/mixing. An appropriate model for
this type of flow is a lubrication/thinfilm displacement model,
which models the evolving stratification. However, the neglect
of inertial effects in such models limits their applicability.
Rather
than use 2D or 3D simulation for these flows, which is particularly
costly for yield stress fluids, it is of interest to model these
flows using reduced models. On the other hand, we would like to
predict the stability and displacement characteristics of the
flow. Here we present our current work on modelling these flows.
A recent approach to modelling weak inertial effects is the weighted
residual method of RuyerQuil Manneville [1]. This has been extended
to twolayer Newtonian channel flows by Amaouche et al. [2]. The
basic approach gives a 2nd order accurate approximation to the
interface height and volumetric fluxes, while reducing the model
complexity to two coupled 1D conservation laws, and also reproducing
the (longwavelength) stability characteristics of the 2D flow.
We show how this approach is extended to twolayer flows in which
both fluids are of HerschelBulkley type. Although the derivation
is complex, the resulting equations have the same structure as
the Newtonian fluid model. We present examples from the analysis
of these equations and discuss possible generalisations.
References
[1] C. RuyerQuil and P. Manneville, Improved modeling of flows
down inclined planes, Eur. Phys. J., B 15, (2000) 357369.
[2] M. Amaouche, N. Mehidi, and N. Amatousse, Linear stability
of a twolayer film flow down an inclined channel: A secondorder
weighted residual approach. Phys. Fluids 19 (2007) 084106.1084106.14.
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Alex Hay, Department of Oceanography, Dalhousie University
On the Dynamic Interactions between Turbulent Oscillatory Boundary
Layers and Mobile Sediment Beds
Using
as a basis results from experiments carried out both in the real
ocean and in the laboratory, including measurements with a new
multifrequency Doppler profiler developed in collaboration with
Len Zedel at Memorial University, the interactions among wave
and current forcing over beds of mobile sediment, the different
patterns of mobile bed adjustment, and the vertical and temporal
structure of flow and turbulence in the wave bottom boundary layer,
are presented and discussed. The purpose of the talk is to indicate
that the field of mobile bed dynamics in nearshore and continental
shelf environments is entering a transformative stage, one in
which the measurement tools have advanced to the point that meaningful
comparisons between observations and numerical simulations are
within reach.

Tiger
Jeans, University of New Brunswick
Analysis of a Lift Based Ocean Wave Energy Converter using Unsteady
Reynolds Average NavierStokes Simulations
The
viscous wave generation properties of a novel lift based wave
energy converter, namely, a Cycloidal turbine, are investigated.
The energy converter consists of two hydrofoils attached parallel
to a horizontal main shaft at a radius. The main shaft is aligned
parallel to the wave crests and submerged at a fixed depth. The
local flow field induced by the incident wave will cause the hydrofoils
to rotate about the main shaft. The orientation of each hydrofoil
is adjusted to produce the desired level of bound circulation.
Previous twodimensional potential flow simulations demonstrated
99% and 77% wave cancellation in straight crested regular and
irregular deep ocean waves, respectively. Here the unsteady RANS
equations are employed to extend the analysis to include nonlinear
viscous effects. Free surface capturing is achieved using the
volume of fluid method. CFD results are validated against 1/10
scale model experiments and potential flow simulations. Resulting
surface waves, hydrofoil bound circulation, and shaft torque are
determined for fixed angles of incidence.
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Sarah
Hormozi
Department of Mathematics, University of British Columbia
Coauthors: I.A. Frigaard & N.J. Balmforth
A mathematical model to predict the shape of thickened tailings
Surface
deposition of mine tailings with high water content entails not
only the risk of catastrophic failure and environmental damage
but is also waste of water resources. Therefore, thickened tailings
deposition is a fast growing technology in both the mining and
oil sands industries. Prediction of the tailings profile is essential
in calculating the storage capacity and designing the thickening
process. However, this prediction is a challenging problem due
to complex rheology of thickened tailings and the role of a wide
range of mechanisms such as sedimentation, consolidation, desiccation
(evaporation), etc. Existing models poorly predict the shape of
tailings disposal.
We present preliminary results of a mathematical model to predict
the shape of thickened tailings. Thickened tailings are modelled
as a viscoplastic fluid containing coarser solid particles. The
system of fluid and solid particles is modelled as a single phase
using a mixture model with HerschelBulkley constitutive law,
but modified to include the effect of solid volume fraction on
viscosity and yield stress. A thinlayer theory is developed to
explore the effects of sedimentation, consolidation and yield
stress on the spreading dynamics of the thickened tailings.
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Hossein
Amini Kafiabad
Mechanical Engineering, McGill University
Coauthors: George Haller and P. W. Chan
Lagrangian Detection of Aerial Turbulence for Landing Aircraft
Recent
studies have shown that aerial disturbances affecting landing
aircraft have a coherent signature in the Lagrangian particle
dynamics inferred from Light Detection And Ranging (lidar) velocity
scans. Specifically, attracting Lagrangian Coherent Structures
(LCSs) mark the intersection of localized material upwelling with
the cone of the lidar scan. Here we test the detecting power of
LCSs on historical landing data and corresponding pilot reports
of disturbances from Hong Kong International Airport (HKIA). We
find that a specific LCS indicator, the gradient of the FiniteTime
Lyapunov Exponent (FTLE) field along the landing path, provides
an efficient marker of turbulent upwellings. In particular, Receiver
Operating Characteristics (ROC) graphs show that projected FTLE
gradients approach the efficiency of the wind shear alert system
currently in operation at HKIA, even though the latter relies
on multiple sources of data beyond those used in this study.
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to top

(C)
P.N.Kaloni, Dept. of Mathematics and statistics University of
Windsor
Magnetic Fluids: A critical study of the Constitutive Equations
Magnetic
flids are stable colloidal suspensions of fine ferromagnetic mono
domain nanoparticles in a nonconducting carrier fluid.These fluids
have found several industrial applications in cooling and damping
of loud speakers,in shock absorbers in jet printing and in biomedical
applications,such as
drug targeting.These fluids are different from the fluids which
are dispersions of micon sized particles,and in which the main
interest is related to the nonNewtonian propertiesvery much like
in polymer fluids. In the recent years a variety of constitutive
equations have been proposed to describe these fluid.Some of these
are phenomenological,some are based on thermodynamics,some of
these are based upon the internal rotation of the particle,some
are based on the statistical mechanics consideration,and some
are based upon the dynamic meanfield theory. There are very few
experimental results available,and thus the predictions based
upon the different theories can not be properly described and
discussed. Our purpose here is to first discuss critically the
developmement of these equations and then solve a bechmark problem
in all theories,for which,if not complete,some experimental information
is available.
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Ida Karimfazli, University
of British Columbia
Coauthors: I. A. Frigaard
On
the natural convection of stratified Bingham fluid in a vertical
channel with differentially heated side walls
Vertical
ducts filled with yield stress fluids and with differentially heated
walls are found in the drilling and cementing of oil wells, as well
as potentially in other construction geometries and geophysical
contexts. In these settings it is of interest to determine whether
or not the thermal heating effects are sufficient to promote fluid
motion.
As an archetypical flow we consider a vertical plane channel flow
between two differentially heated walls, separated by a distance
L. In addition to a constant temperature difference, there is a
linear vertical temperature variation imposed at the walls. This
configuration was studied by Bergholz(1978) in the case of Newtonian
fluids. The base flow is governed by two dimensionless parameters:
a stratification parameter and a Bingham number. Of academic interest
is the fact that for sufficiently large stratification parameter
and small Bingham number it appears we can find infinitely many
unyielded plug regions  a peculiarity for a steady flow in a finite
domain.
We present an analysis of onset of flow and a classification of
base flow at various stratification parameter and Bingham numbers.
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Richard
Karsten, Acadia University
Analysis of Tidal Turbine Arrays in the Digby Neck Passages
Coauthors: Mitchell O'FlahertySproul, Joel Culina, Justine
McMillan, Greg Trowse, Alex Hay
The
Nova Scotia government has approved tidal power CommunityFeedinTariffs
for two passages along Digby NeckDigby Gut and Petit Passage.
Digby Gut is a passage connecting the small, enclosed Annapolis
Basin to the Bay of Fundy. It has tidal currents up to 3 m/s.
On the other hand, Petit Passage is a passage between the large,
open St. Mary's Bay and the Bay of Fundy. It has strong tidal
currents that can exceed 5 m/s. The critical difference is that
altering the flow in Digby Gut strongly affects the surrounding
tides, while altering the flow in Petit Passage does not. Thus,
while the passages have a similar size and volume flux, the theoretical
maximum extractable power for Digby Gut is over 200 MW but for
Petit Passage is only 40 MW! Using validated, high resolution,
3D numerical models of the tides and tidal currents through the
passages, we examine the power generation potential of turbine
arrays in these two passages and calculate the impact that power
extraction will have on the currents and tides. Finally, we examine
how arrays of instream turbines should be designed for each passage
based on their geometry and tidal dynamics.
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(Talk Cancelled) Brendan Keith,
Department of Mathematics and Statistics,
McGill University
Coauthors: Hossein Amini Kafiabad (Department of Mechanical Engineering,
McGill University)
Nonlinear dynamics and chaotic motion of a nonspherical single
bubble surrounded by viscoelastic fluid
We
study nonlinear dynamics of a nonspherical, acoustically driven
gas bubble surrounded by a viscoelastic fluid. The Maxwell fluid
is picked as the model for the surrounding liquid to include the
simultaneous effects of viscosity and elasticity. For our model,
we derive the governing equations of motion by perturbing the
spherical configuration of the bubble in terms of the spherical
harmonic modes. In this, a robust numerical approach enables us
to capture the bubble behavior in very high amplitudes of excitation.
The stability of spherical modes as well as their bifuractions
are then studied by changing physical parameters such as Debora
number, Reynolds number, and amplitude and frequency of excitation.
Moreover, the onset and characteristics of chaos in the bubble
dynamics are investigated in our analysis. Our results show that
some important impacts of rheology on the bubble behavior can
only be revealed by taking the nonsphericalities into account.
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Boualem
Khouider, University of Victoria
Convective momentum transport and multiscale organization of
convectively coupled tropical waves
Convection
in the tropics is organized into a hierarchy of scales ranging
from the convective cells of 1 to 10 km, to mesoscale cloud clusters
of 100 to 500 km, to synoptic scale waves of 1000 to 5000 km to
to planetary scale waves of 10,000 to 20,000 km. The atmospheric
planetary scale variability, in winds and precipitation, is dominated
by an intraseasonal oscillation of 40 to 60 days known as the
MaddenJulian oscillation (MJO) while convectively coupled Kelvin
waves (CCKWs) dominate the synoptic scale variability. The MJO
disturbance starts in the Indian ocean warm pool as a standing
wave and slowly propagates eastward at roughly 5 m/s. The MJO
has a significant impact on weather and climate patterns and extremes
in the tropics and extratropics yet contemporary global climate
models (GCMs) simulate poorly the MJO and organized convective
systems in general. CCKWs are trapped in the vicinity of the equator
and move eastward at 15 m/s. Multiscale CCWs are often embedded
in each other like Russian dolls; The MJO often appears as an
envelope of synoptic and mesoscale waves and mesoscale waves often
develop inside Kelvin waves. The complex interactions across scales
associated with this multiscale organization remain poorly understood
and misrepresented in climate models.
Convective
clouds not only release heat and moisture into the troposphere
but they also deposit momentum due to the underlying eddies. This
latter phenomenon known as convective momentum transport (CMT),
applies also to turbulent fluxes associated with mesoscale and
synoptic scale convective organized systems when regarded from
larger scales. However, while the small eddies, associated with
parcel lifting, result essentially in largescale momentum damping,
a.k.a cumulus friction, due to their chaotic nature just like
the usual fluid dynamics turbulence, there is enough observational,
numerical, and theoretical evidence that the CMT associated with
meso and synopticscale convective systems can significantly
accelerate and/or decelerate the ambient flow. In this talk, we
present some numerical simulations of CCKWs, in a channel domain,
using the WRF model that shows evidence of coherent CMT fluxes
from mesoscale convective systems embedded within the large scale
Kevin wave. We then propose a simple model parametrization that
takes into account the effect of CMT from unresolved mesoscale
convective systems in GCMs. It is demonstrated, in the context
of a toy GCM, that mesoscale CMT helps the organization of and
strengthens substantially the planetary and synoptic scale waves,
i.e., the MJO and Kelvin waves.
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Mary
Catherine Kropinski (SFU)
Coauthors: Nilima Nigam
Fast Integral Equation Methods for the LaplaceBeltrami Equation
on the Sphere
Integral
equation methods for solving the LaplaceBeltrami equation on
the unit sphere in the presence of multiple "islands"
are presented. The surface of the sphere is first mapped to a
multiplyconnected region in the complex plane via a stereographic
projection. After discretizing the integral equation, the resulting
dense linear system is solved iteratively using the fast multipole
method for the 2D Coulomb potential in order to calculate the
matrixvector products. This numerical scheme requires only O(N)
operations, where N is the number of nodes in the discretization
of the boundary. The performance of the method is demonstrated
on several examples, including the motion of several point vortices
on the sphere.
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Michael
Lindstrom, Brian Wetton, [A third author may be added
Modelling
Nuclear Fusion Reactors: Numerical Approximations of Fluid Dynamics
Equations inside a Moving Domain
A
modern engineering design for harvesting nuclear energy involves
the implosion of a sphere of liquid lead with hydrogen plasma
filling its central axis. The intense pressure generated by the
imploding lead is aimed at fusing the plasma, releasing energy.
The mathematical modeling of such an apparatus involves a careful
interplay between fluid dynamics and plasma physics, along with
suitable numerical approximation schemes for nonlinear hyperbolic
PDEs with moving boundaries. Our work begins with a simplified
onedimensional model with a moving interface at the left and
right, within which there is liquid lead. This talk will present
our current work, where a loworder numerical scheme for hyperbolic
PDEs is used to couple mass and momentum conservation, the lead
equation of state and elementary plasma properties, in order to
predict the compression of the plasma. In the process, we also
investigate the optimal implementation of the boundary conditions.
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Frances
Mackay, Colin Denniston
The University of Western Ontario
Liquid Crystal Induced Colloidal Deformation
We
numerically investigate the behavior of 2D deformable particles
immersed in a liquid crystal. A beadspring model is used to represent
the particles, while the liquid crystal is modeled using the latticeBoltzmann
method. Perpendicular anchoring is assumed at the particle surface,
leading to distortions in the bulk liquid crystal orientation.
These distortions result in nonspherically symmetric local forces
acting on the elastic particle membrane, causing a deformation
of the particle. We present the resulting particle shapes for
a range of surface elasticities, and investigate the interaction
between pairs of particles.
Peter
Minev,
University of Alberta
Coauthors: JeanLuc Guermond
Massivelyparallel direction splitting techniques for the incompressible
NavierStokes equations with a variable density and viscosity
A
new directionsplittingbased fractional time stepping for solving
the incompressible NavierStokes equations will be discussed.
The main originality of the method is that the pressure correction
is computed by solving a sequence of one onedimensional elliptic
problem in each spatial direction. The method is unconditionally
stable, very simple to implement in parallel, very fast, and has
exactly the same convergence properties as the Poissonbased pressurecorrection
technique, either in standard or rotational form. The onedimensional
problems are discretized using central difference schemes which
yield tridiagonal systems. However, other more accurate discretizations
can be applied as well. The scheme is further extended to allow
for the computation of flows with nonconstant density/viscosity
without the need to recompute the matrix and its Schur complement
at each time step. This is achieved via a perturbation of explicit
schemes which stabilizes them in the spirit of the direction splitting
schemes discussed above.
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James
Munroe, Memorial University of Newfoundland
Coauthors: Sylvain Joubaud, Philippe Odier, Thierry Dauxois
Measuring Parametric Subharmonic Instability in Internal Waves
Parametric
subharmonic instability is a mechanism of energy transfer between
internal waves from large to small spatial scales. In this type
of resonant triad interaction, a parent wave of higher frequency
destabilizes leading to the growth of two daughter waves with
lower frequencies. In a laboratory experiment, a fulldepth wave
generator forces a high frequency vertical mode1 internal wave
and parametric subharmonic instability is observed. The growth
rate of the instability is measured using a timefrequency analysis
and compared with theoretical predictions.
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(C)Lidia
Nikitina, Carleton University, School of Mathematics and Statistics
Coauthors: Lucy Campbell
Propagation of Rossby waves in a tropical cyclone
Observational
analyses of hurricanes in the tropical atmosphere indicate the
existence of spiral rainbands which propagate outwards from the
eye and affect the structure and intensity of the hurricane. These
disturbances may be described as vortex Rossby waves. Under certain
conditions, two concentric rings of highintensity wind (concentric
eyewalls) develop. The outer or secondary eyewall appears to be
related to wavemeanflow interactions near the critical radius
where the mean flow angular velocity matches the phase speed of
the waves. In this study we carry out asymptotic analyses to examine
the evolution of the interactions near the critical radius in
some twodimensional configurations on an fplane and a betaplane.

(C)
Mohammad Niknami, Department of Mechanical and Materials Engineering
, Western University
Coauthors: Roger Khayat
The stability of natural convection in a nonFourier fluid layer
between two parallel vertical plates is investigated theoretically.
The two plates are maintained at different constant temperatures
and their length is assumed to be tall enough so they can be regarded
as infinite length in the vertical direction. SinglePhaseLag
heat conduction relation is used for the heat equation, in an
attempt to model the convection of nonFourier fluids. This means
that the traditional Fourier law of heat conduction is not applicable
here anymore. Unlike the horizontal fluid layer flow (RayleighBenard
convection), vertical motion in the base flow in the vertical
slot case will affect the critical conditions for the onset of
secondary convection. The critical Grashof number for instability
to occur is obtained in the case of some different Prandtl and
Cattaneo numbers.
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Robert
G. Owens, Département de mathématiques et de statistique,
Université de Montréal
Coauthors: Yasmine Tawfik
Oscillations in realistic models of large capillary networks:
physical or numerical?
Fluctuations
in red cell velocities and concentrations observed in capillary
networks have traditionally been ascribed to biological control
(precapillary sphincters, vasomotion) and statistical variations
in cell and vessel properties (Fung (1973)). However, it is now
believed that hemorheological factors in the network may also
influence temporal variations in the flow parameters. The development
of mathematical models of the microvasculature has allowed the
dynamics in large networks to be studied in the absence of biological
control. Are fluctuations in flow parameters in such models physical,
an artefact of an unrealistic model or are they (at least in part)
numerical?
Although it has been proved mathematically in the case of small
networks and a simple model of microvascular blood flow that Hopf
bifurcations of the equilibrium solution can occur (see, for example,
Geddes et al. (2007)), the situation for more realistic (and therefore
more complicated) models and large networks is less clear and
no consideration seems to have been given to the role that the
choice of numerical algorithm employed may play in the observed
results. Since the pioneering paper of SchmidSchönbein et
al. (1980), the Picardtype numerical algorithm adopted by many
authors for solving blood flow in the microcirculation has been
to solve alternately at each time step a linear problem for the
nodal pressures and a nonlinear problem for the determination
of the segment hematocrits and apparent viscosities (see, for
example, Pries et al. (1990), Kiani et al. (1993, 1994), Obrist
et al. (2010)). Kiani et al. (1993, 1994) reported the appearance
of oscillations in flow parameters that apparently were caused
by hemodynamic factors at network bifurcations alone, and not
due to fluctuating boundary conditions, vasomotion or other forms
of biological control.
In this talk we will study blood flow through large microculatory
networks using the model of Pries et al. (1990) and two different
numerical algorithms. The first is the traditional Picardtype
method mentioned already and the other is a new iterative scheme
that allows us to solve the linear and nonlinear parts of the
problem together in an efficient manner. This is done using a
quasiNewton method for the outer iterations and preconditioned
conjugate gradient and GMRES methods for the inner iterations.
We compare the results of the two approaches in order to ascertain
to what extent the oscillations that have been observed using
the traditional scheme may be attributable to this choice of numerical
method.
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Dominique
Pelletier (Ecole Polytechnique Montreal)
Coauthors: Stephane Etienne
Verification of codes and simulations for unsteady incompressible
flows on deforming domains
We
discuss the method of manufactured solution (MMS) for code verification
of incompressible flows on deforming domains ( free surface flows,
fluid structureinteractions, and fluid rigid solid interaction).
MMS provides closed form solutions to the flow PDEs so that the
error can be computed and it convergence monitored by grid and
timestep refinement studies. Techniques are described for high
order implicit
RungeKutta time integrators.

Nicolas
Perinet, University of Ontario Institute of Technology
Coauthors: Gregory M. Lewis, Lennaert van Veen
Secondary Transitions and Instabilities in Geophysical Fluids
We
track invariant solutions in a model of the differentiallyheated
rotating annulus, an experiment that presents analogies with atmospheric
circulation. The rotation rate of the annulus is of fundamental
importance. Indeed, low rotation rates generate steady flows similar
to those observed in the tropical atmosphere. An increase in the
rotation rate causes these stationary solutions to bifurcate to
periodic solutions taking the form of travelling waves. A secondary
bifurcation leads to quasiperiodic flows such as mixedmode or
amplitudevacillating flows, which are similar to the atmospheric
flows of temperate regions. The study involves numerical continuation
methods in a flow modeled by the threedimensional NavierStokes
equations in the Boussinesq approximation.
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Francis
Poulin, University of Waterloo
Coauthors: Guillaume Lapeyre, Laboratoire de Météorologie
Dynamique
Exploring Vortex Asymmetry in a Simplified TwoLevel QG+1
Model
QuasiGeostrophy
(QG) has played a pivotal role in exposing the underlying dynamics
of the largescale Atmosphere and Oceans. Even today where so
much research is numerically based, QG is still very popular because
of how efficient it is in describing motions dominated by rotation.
Over a decade ago a nextorder correction to QG, aptly named QG+1,
was derived that allowed for some nonQG effects while still remaining
very simple compared to the primitive equation models. Here, we
present a reduced version of QG+1 that only has two vertical levels.
This includes one barotropic and one baroclinic mode that can
exhibit vortex asymmetry. By studying the dynamical balances we
determine the mechanisms that can achieve either a dominance of
cyclones or anticyclones and demonstrate this through numerical
simulations of freelyevolving turbulence.
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Bartosz
Protas, McMaster University
Coauthors: Diego Ayala (McMaster University)
Maximum Palinstrophy Growth in 2D Incompressible Flows
This
investigation is a part of a broader research effort seeking to
construct solutions of the NavierStokes system in 2D and 3D which
can saturate certain analytically obtained bounds on the maximum
growth of enstrophy and palinstrophy. This research is motivated
by questions concerning the possibility of finitetime blowup
of solutions of the 3D NavierStokes system where such estimates
play a key role. We will argue that insights concerning the sharpness
of such estimates can be obtained from the numerical solution
of suitablydefined PDE optimization problems. Following a review
of the available analytical estimates for the maximum instantaneous
and finitetime growth of palinstrophy in 2D flows, we will present
computational results concerning realizability of such growth
in actual flows.
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(C)
Bryan Quaife, University of Texas
Coauthors: George Biros (University of Texas)
Boundary Integral Methods for Inextensible Vesicle Dynamics
in 2D
A
boundary integral method for simulating inextensible vesicles
in a 2D viscous fluid was developed by Veerapaneni et. al. Recent
extensions include developing preconditioners, implementing a
nearsingular integration strategy, and allowing for vesicles
with different bending moduli. The goal is to run simulations
with a high concentration of red blood cells and platelets.
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(C)
A. Roustaei
UBC Mechanical Engineering Department
Coauthors: I.A. Frigaard
Onset of fouling in channels with uneven walls
We
consider the pressure driven flow of a Bingham fluid along a channel
with uneven walls. We are interested in the situation where the
fluid gets stuck to the wall of the channel in the widest part.
This could be a typical flow that occurs in many industrial applications
related to oil and gas wells, e.g. drilling and cementing. In
industries such as food processing, such residual deposits represent
a health hazard. We represent the channel wall by a sinusoidal
variation. The Stokes problem is solved numerically a finite element
based discretization and the augmented Lagrangian method. As the
(channel wall) wave amplitude increases, a static zone appears
on the widest section of the channel. We study the formation of
this static zone and it's dependence on a wide range of the three
dimensionless parameters of the problem: the Bingham number, channel
aspect ratio and wave amplitude. We observe some interesting features
in the flow pattern and velocity field, e.g. the final flow geometry
of two different channels can be quite similar when the static
zone exists. Also some accelerating flow regions are found in
the diverging part of the channel, which is counter intuitive.We
outline our attempts at predicting some of these features analytically.
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(C)
Amir Sayed, Carleton University
Coauthors: Lucy Campbell (Carleton University)
Generation of Internal Gravity Waves by Convection in the
Atmosphere
Internal
gravity waves affect the general circulation of the atmosphere
and hence it is important to understand their generation, propagation
and interactions in order to represent them correctly in weather
prediction and climate models. The primary mechanisms for gravity
wave generation are convection in the lower atmosphere and topography;
however, the mechanisms for convective generation are not fully
understood. In this study we develop a twolayer model of internal
gravity waves over convective vortices and use weaklynonlinear
analyses and numerical simulations to obtain approximate solutions
and investigate some of the current hypotheses for convective
generation mechanisms.
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Samuel Shen, San Diego State University
Uncertainties, Trends, and Hottest and Coldest Years of US Surface
Air Temperature Since 1895
This
lecture discusses the sampling error variances of gridded monthly
US Historical Climatology Network Version 2 (USHCN V2) timeofobservation
bias (TOB) adjusted data. Our analysis of mean surface air temperature
(SAT) assesses uncertainties, trends, and the rankings of the
hottest and coldest years for the contiguous United States in
the period of 18952008. Data from the USHCN network stations
are aggregated onto a latitudelongitude grid by an arithmetic
mean of the stations inside a grid box. The sampling error variances
are smaller (mostly less than 0.2 (degrees celcius)x2 over the
eastern US where the station density is greater, and larger (with
values of 1.3 (degrees celcius)x2 for some grid boxes in the earlier
period) over mountain and coastal areas. In the period of 18952008,
every month from January to December has a positive linear trend.
February has the largest trend of 0.162 degrees celcius /decade,
and September has the smallest at 0.020 degrees celcius/decade.
The three hottest (coldest) years measured by the mean SAT over
the US were ranked as 1998, 2006, and 1934 (1917, 1895, and 1912).
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Raymond
Spiteri, Computer Science, University of Saskatchewan
Coauthors: Ahmed Kaffel
Modeling and numerical simulation of particulate flows in
fluidized beds
Gassolid
fluidized beds are widely used in the chemical, petroleum and
energy industries. For instance, fluid catalytic cracking which
is the process of almost every oil refinery, consists of fluidized
beds on the order of meters. At present, the design and scaleup
of such fluidized bed reactors are mostly fully empirical processes,
owing to limited insight into the fundamentals of gassolid flows
at different scales. In particular, the collisions forces, drag
forces, dissipation, and solidwall interactions are not well
understood. For this reason, many preliminary tests on pilotscale
model reactors have to be performed, which is a timeconsuming
and expensive activity. To aid this design process, computer simulations
can clearly be a useful tool. However, a major difficulty in modeling
lifesize fluidized beds is the large separation of scales where
the largest flow structures are on the order of meters but depend
on the solidsolid and solidgas interactions that take place
on the order of millimeters or even micrometers. To describe the
time evolution of both phases and predict the flow behavior of
gassolids flows of systems at large scales, we study issues of
modeling and simulation of particulate flows in fluidized beds
and compare with available experimental data.
A mathematical model for twophase gas particle flow in a fluidized
bed is developed from the basic principles of conservation of
mass and momentum. It consists of a set of partial differential
equations with coupling and interaction between the two phases
and assumes incompressibility in both solid and gas phases, with
equal particle diameters. Numerically, we solve the fluid phase
continuity and momentum equations following an Eulerian approach
and the particle motion following a Lagrangian approach. We show
that the flow structure and its evolution in various flow regimes
can be reproduced from these numerical simulations by including
the competition between particle collisions and particlefluid
interaction.
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Marek
Stastna, University of Waterloo
The effects of the Earth's rotation on large amplitude internal
waves
The
effects of the Earth's rotation on linear waves in a continuously
stratified fluid have been known for many decades. The central
result is the lower bound on frequency which implies that the
phase speed of rotation modified waves is potentially unbounded
(even though the more physically grounded group speed remains
bounded). Recent studies have led to a developing understanding
of how the linear results carry over to internal solitary waves.
I will review the published results, showing examples of the phenomenon
of overtaking solitary waves, as well as more chaotic phenomena.
I will subsequently discuss more recent work on the generation
of waves over topography by supercritical flow that leads to the
astonishing prediction that in the presence of rotation, supercritical
flow over topography in the coastal ocean can lead to the generation
waves with an amplitude in excess of 40 meters (in water 100 meters
deep) at a distance of 100 kilometres from the obstacle.
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Catherine
Sulem, University of Toronto
Coauthors: Walter Craig and Philippe Guyenne
Coupling between internal and surface waves in a twolayers fluid
Un
Internal
waves occur within a fluid that is stratified by temperature or
salinity variation. They are commonly generated in the oceans,
and large amplitude, long wavelength nonlinear waves can be produced
in the interface and propagate over large distances. In some physically
realistic situations, the visible signature of internal waves
on the surface of the ocean is a band of roughness, sometimes
referred to as a ‘rip’ which propagates at the same
velocity as the internal wave, followed after its passage, by
the ‘mill pond’ effect, the complete calmness of the
sea. We propose an asymptotic analysis of the coupling between
the interface and the free surface of a two layers fluid in a
scaling regime chosen to capture these observations. In particular,
we describe the rip region of the free surface as being generated
by the resonant coupling between internal solitons and the freesurface
wave mode. We also give an explanation of the mill pond effect
as the result of a strong reflection coefficient for freesurface
waves in the modulational regime, in a frame of reference moving
with the internal soliton.
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YuHau Tseng, York University
Coauthors: KuoLong Pan, MingChih Lai
Immersed Boundary Method for Headon Droplets Collision and Phagocytosis
with Surfactant
A
numerical method based on the immersed boundary method is proposed
to simulate the collision between two identical water droplets
mixed with surfactant. In dynamics of water droplets collision,
the bouncing phenomenon was not observed for pure water in the
atmosphere, but was found for water droplets with surfactant in
experiments. In relevant literatures, this regime was conjectured
to be caused by the nonuniform distribution of surfactant and
hence the gradient of its concentration near the droplet surface,
known as Marangoni effect. This could substantially affect the
fluid motion by varying such critical mechanisms as the interfacial
deformation of liquid and draining dynamics of gas intervening
between the interfaces. Innumerical experiments, a numerical method
to handle the solubility of the surfactant in the
droplets is verified, a series of numerical tests with consideration
of intermolecular forces are compared to underline the dominance
of the Maragoni effect, and numerical results produced by
different amount of surfactant are presented. In second part,
phagocytosis is one of endocytosis functions which captures vesicles
or microorganism into a cell. In phagocytosis, several kinds of
surfactant coexist and chemical reaction among these surfactant
derives a great diversity of interface dynamics. A simple mathematical
model and corresponding numerical method for
phagocytosis, and the preliminary results will be presented.
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José
Urquiza (GIREF, département de mathématiques et
de statistique, Université Laval )
Coauthors: Bocar Wane and André Fortin
Anisotropic mesh adaptation and iterative methods for free
surface turbulent flows.
We
show how iterative methods based on the hierarchical quadratic
finite elements and an anisotropic mesh adaptation strategy can
be used to solve efficiently free surface turbulent flow problems.
For the turbulence modeling, a logarithmic formulation of the
kepsilon model is used, and the free surface is computed using
the level set method.The whole strategy is applied to various
problems ranging from a simple manufactured solution to 3D flows
around obstacles piercing the free surface.
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Henry van Roessel, University of Alberta
Two species coagulationannihilation
The
irreversible growth of a species of particles by the successive
merger of clusters of particles occurs in many fields of science,
such as polymer chemistry, colloid science, cloud dynamics and
star formation. The most popular meanfield model describing such
phenomena is Smoluchowski's coagulation equation.
Now consider the situation of two distinct species, where two
clusters of the same species will merge or coalesce when they
come together, but where clusters of different species will be
annihilated when they come together. This situation can be modelled
by a generalized form of Smoluchowski's coagulation equation.mThe
long time behaviour of this scenario will be discussed.
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Lennaert van Veen, University of Ontario
Institute of Technology
Coauthors: Genta Kawahara, Osaka University, Japan.
The onset of sustained turbulence in channel flow
The
motion of a fluid trapped between two parallel, moving walls,
otherwise known as Couette flow, is known to be laminar at small
forcing and turbulent at large forcing. However, the laminar state
is a dynamically stable equilibrium at all Reynolds numbers. There
is no generally accepted theory for the transition to turbulence
in the presence of a stable laminar state. In this presentation
I will review some proposed theories, focussing on the ëdge
state" hypothesis and in particular on the recent discovery
of solutions homoclinic to edge states. Such solutions might explain
irregular turbulent bursting near the transition threshold and
help us define a critical Reynolds number.
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Mike Waite (Waterloo)
Buoyancy scale dynamics in direct numerical simulations of
stratified turbulence
New
direct numerical simulations (DNS) of strongly stratified turbulence
will be discussed. Stratified turbulence presents a particular
computational challenge, because stable stratification tends to
reduce the characteristic vertical scale of the turbulence. As
a result, as the Froude number of a flow is reduced, higher Reynolds
numbers are necessary to obtain a turbulent cascade. The classical
picture of such flows is that there is a transition from stratified
to isotropic turbulence below the Ozmidov scale. However, recent
simulations with ad hoc smallscale dissipation have shown that
a transition occurs at the (larger) buoyancy scale U/N, where
U is the r.m.s. velocity and N is the buoyancy frequency. Here,
I will show that these transitions are also present in DNS, even
at relatively modest Reynolds numbers. They appear to result from
KelvinHelmholtz instability of the largescale quasihorizontal
flow, and corresponds to a direct, nonlocal transfer of energy
from large to small scales.
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Jonathan
Wylie (City University of Hong Kong)
Coauthors: Huaxiong Huang and Robert Miura
Asymptotic Analysis of a Viscous Drop Falling Under Gravity
Despite
extensive research on extensional flows, there is no complete
explanation of why highly viscous fluids falling under gravity
can form such persistent and stable filaments. We therefore investigate
the motion of a slender axisymmetric viscous drop that is supported
at its top by a fixed horizontal surface and extends downward
under gravity. We consider the full initialboundaryvalue problem
for arbitrary initial shape of the drop in the case in which inertia
and surface tension are initially negligible. We show that, eventually,
the accelerations in the thread become sufficiently large that
the inertial terms become important. We therefore keep the inertial
terms and obtain asymptotic solutions forthe full initialboundaryvalue
problem. The asymptotic procedure requires a number of novel techniques
and the resulting solutions exhibit surprisingly rich behavior.
The solution allows us to understand the mechanics that underlies
highly persistent filaments.
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Xiaohua Wu,Royal Military College of Canada
Coauthors: Parviz Moin, Stanford University
Visualization of flatplate boundary layer bypass transition
with continuous freestream turbulence
We introduce the concepts of bypass transition in the narrow sense,
and bypass transition in the general sense. A database with sufficient
spatial information and reasonable temporal information has been
created using verylargescale direct numerical simulation on
an incompressible, smooth flatplate boundary layer with mild
continuous freestream turbulence. Inlet freestream turbulence
intensity is 3 percent, and decays with distance according to
the 1/2 powerlaw to 0.8 percent by the exit station of momentum
thickness Reynolds number 2000. Statistics in the transitional
region are compared with those from previous bypass transition
experiments and from theory. The evaluation demonstrates that
the present transitional regime is a representative bypass transition
in the narrow sense. Visualization of the bypass transition process
indicates that the transition mechanism under mild continuous
freestream turbulence bears good similarity with the secondary
instabilities of natural transition as discussed in Klebanoff,
Tidstrom, Sargent (1962), Herbert (1988), Bake, Meyer, Rist (2002).
Specifically, quasispanwise structures arise inside the boundary
layer through receptivity. Some of these structures develop into
Lambda vortices, which are subsequently stretched and detached
into pairs of obliquely oriented quasistreamwise leg vortices.
Hairpin packet forms within the detached L vortex, and breakdown
ensues with the emergence of infant turbulent spot, which in itself
is the hairpin packet with chaotic fluctuations. This process
differs from the streak growth, streak secondary instability,
and streak breakdown scenario reported in many previous bypass
transition studies. The present mechanism is consistent with our
previous work on boundary layer with discrete patches of freestream
turbulence. It is therefore quite possible that boundary layer
bypass transition, at least a subcategory of it, might be loosely
treated, and probably modeled, as the secondary instability of
natural transition with merely the TSwave being circumvented.
Razvan Fetecau,Simon Fraser University
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David Zingg
University of Toronto Institute for Aerospace Studies
Coauthors: David Del Rey Fernandez, Hugo Gagnon
Recent Progress in Computational Aerodynamics for Future Aircraft
Design
This
talk will present some recent progress in computational aerodynamics,
including aerodynamic shape optimization. Topics to be discussed
will include summationbyparts finitedifference operators, superconvergence,
and dual consistency. Moreover, an approach is presented that
combines gradientbased optimization with Sobol sequences to provide
global optimization and a twolevel freeform deformation technique
is described that provides a geometry parameterization suitable
for optimization of unconventional aircraft configurations.
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POSTDOCS

Maurizio Ceseri, Simon Fraser University
Coauthors: John Stockie
Mathematical modeling of sap flow in maple trees
In
early spring, sap in maples starts flowing in the vessels of the
tree after being dormant for the whole winter. The flux onset
is triggered after ambient temperature fluctuates around the freezing
temperature for several days. When temperature is below the freezing
point of sap, ice starts forming in the interior wall of the air
filled fibers of the tree drawing sap from the adjacent vessels.
The ice compresses the air bubble into the fiber as it grows.
Once ambient temperature rises above the freezing point, the above
mechanism is reversed. We present here a compartment model describing
the process for a single fiber and a vessel element.
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George M Homsy,University of British
Columbia
Coauthors: Harish N Dixit
Cylinders on flat and curved interfaces: role of surface tension
We
consider cylindrical particles floating on a fluid interface and
investigate the role of surface tension in generating lateral
forces on the particles. A single particle on a flat interface
assumes a static equilibrium such that the weight of the particle
is balanced by surface tension and buoyancy forces. But in the
presence of a background curvature, the particle experiences unbalanced
lateral forces. In the absence of gravity, the lateral force varies
as the gradient of curvature of the background interface. To account
for gravity, we employ a systematic perturbation procedure in
B1/2, where B is the Bond number, to obtain analytical formulae
for lateral force on a single particle. We then extend the analysis
to obtain capillary attraction forces in the presence of multiple
particles. Our procedure recovers the well known Nicolson approximation
at leading order for attraction between two particles. Finally,
we obtain the capillary forces for an infinite array of cylinders.
This case will be shown to be distinct from the two cylinders
case where we show that using a simple superposition approximation,
as has often been done in literature, may lead to incorrect results.
We will also describe one application of particles on an interface:
dipcoating flow of a particleladen films.

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 Malcolm Roberts (UofA, John Bowman)cancelled
 Nicolas Perinet (UOIT, Greg Lewis)
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(C)Driss
Yakoubi, GIREF, Universite Laval
Coauthors: A. Fortin, J. Urquiza, J. Deteix, E. Chamberland
A hierarchical iterative solver for the NavierStokes equations
We
present in this work an iterative method for the solution of the
incompressible NavierStokes equations. The method was first introduced
in El maliki and Guenette [1]. A second order TaylorHood (P2P1)
element is used for the space discretization where the quadratic
velocity is expressed using a hierarchical basis.
A secondorder backward finite difference scheme is used for the
timederivative. The convection term is linearized using a second
order extrapolation method. The overall method is therefore second
order
in both space and time. The linear system at each time step takes
some special form where the proposed iterative method exploits
this decomposition and can be parallelized in a very efficient
way. The method performs very well
even on anisotropic meshes presenting very elongated elements.
The method is then applied to compute the threedimensional flow
in a stenosis and in a 2 to 1 sudden expansion. In both cases,
we show that there is a symmetry breakup for steady solutions
when the Reynolds number is increased.
References:
[1] A. El Maliki and R. Gu´enette. Efficient preconditioning
techniques for finiteelement quadratic discretization arising
from linearized incompressible Navier–Stokes equations. International
Journal for Numerical Methods in Fluids, 63(12):1394–1420,
2010.
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