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Fluid Mechanics Group  
         

General Information

The nonlinear dynamics of fluid flow is key to phenomena in fields as diverse as astrophysics, biology, engineering, physics and the geosciences. Research at the IAM focusses on practical fluids problems in many of these applications, but also explores fundamental theory of fluid mechanics itself. Specific directions of research include the instabilities encountered in shear flows and vortices, the dynamics of complex fluids, flow problems in industrial processes and the environment, and glacier mechanics. We are always interested to hear from potential graduate students and postdoctoral fellows. We recruit from many different backgrounds, including mathematics, physics, engineering and the geosciences. We often supervise undergraduate thesis projects and take on summer research undergraduate students.

 

Research facilities of the IAM Fluid Mechanics Group include the Laboratory for Complex and Non-Newtonian Fluid Flow (Fluids Lab), which is operated by the IAM faculty in the Mathematics Department. The Lab contains space, tools and equipment for experiments, including several rheometers and other equipment for studying fundamental fluid properties. Recent experiments include skipping and sloshing (the dynamics of skimming stones and reservoirs with movable dams), as well as the pinch-off of pendant drops and liquid bridges of complex fluids.

Complex fluids have microscopic structure that influences the macroscopic flow behaviour. For example, suspended polymers can unravel and intertwine as fluid flows, endowing the material with an effective elasticity; such viscoelastic fluids climb rods rotating in them and extend into strong, fine filaments. Other fluids have networks of interacting particles that build a microstructure capable of holding the fluid up against gravity and other stress; such viscoplastic fluids include mud, hair gel and tomato ketchup.

   
   
Partial coalescence in Newtonian fluids   Simulation of a partial coalescence cycle for a Newtonian drop   Coalescence of a polymeric drop at a decane-PEO solution interface
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Core Faculty

The Fluid Mechanics Group is composed of several core IAM faculty who are actively involved in the IAM activities and supervise IAM students or postdoctoral fellows. Prospective students interested in research in Fluids Mechanics in the IAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests. The Group's research areas include complex fluids, atmospheric and ocean dynamics, geophysics, and engineering fluids.

 
Neil Balmforth
Neil is a Professor in the Department of Mathematics and in Earth and Ocean Sciences. His research interests include geophysical and astrophysical fluid dynamics and complex fluid flow. He has co-organised and directed a variety of programmes in Geophysical Fluid Dynamics, including the summer school at the Woods Hole Oceanographic Institution. Since 2008, Neil has been the Director of the IAM.
Jimmy Feng
Jimmy is a Professor of Mathematics and of Chemical and Biological Engineering. He is interested in the dynamics and applications of complex fluids, such as polymers, liquid crystals, colloids, emulsions, foams and various biological fluids. Jimmy's work is highly interdisciplinary, spanning over applied mathematics, soft-matter physics, chemical engineering and biomedical engineering.
Ian Frigaard
Ian is a Professor of Mathematics and Mechanical Engineering. His research focusses on the mechanics of non-Newtonian fluids, particularly viscoplastic fluids, and in understanding industrial processes that exploit the non-Newtonian fluid properties. Examples of practical applications include oilfield cementing, well control, transport in pipelines, spray forming, etc. Ian's research combines mathematical, experimental and computational approaches.
George "Bud" Homsy
Bud joined the UBC Departments of Mathematics and Mechanical Engineering in 2009. His research interests are in interfacial flows, polymer and viscoelastic fluid mechanics, porous media flows, and in microgravity fluid mechanics. He is currently Deputy Director for the UBC site of PIMS.
Greg Lawrence
Greg is a Professor of Civil Engineering. His main research area is environmental fluid mechanics, with the primary focus on the impact the fluid flow has on inland and coastal waters. He is also interested in hydraulics, hydrodynamic stability and mixing, physical limnology, and water quality management.
Mark Martinez
Mark is a Professor of Chemical and Biological Engineering, interested in multiphase flows and computational fluid dynamics with applications to industrial problems. His main research focus is on investigating the papermaking fibre suspensions, which often exhibit complex behaviour not seen in ordinary fluids such as water. Mark actively collaborates with UBC researchers in Mechanical Engineering, Mathematics and in TRIUMF.
Christian Schoof
Christian is a Professor in the Department of Earth and Ocean Sciences. He is mainly interested in glaciology and in ice-sheet dynamics, which he analyses using various mathematical tools, including PDEs, free boundary problems, applied complex analysis, nonlinear dynamics, perturbation methods, etc. Christian also conducts field work on the site in St. Elias Mountains, collaborating with Gwenn Flowers from Simon Fraser University.
Brian Wetton
Brian's major research area is the numerical analysis of various fluid flow and geometric motion problems. Over the past 10 years, he has done extensive research on fuel cell modelling, collaborating with Ballard Power Systems and MITACS, and is still interested in pursuing other industrial projects. Brian is currently supervising three graduate students in the IAM.
 
 
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Recommended Courses

Research in fluid mechanics prompted the development of many classical and modern techniques of Applied Mathematics. Matched asymptotic expansions and spectral methods for partial differential equations were both developed with fluid problems in mind, and the theory of solitons and the inverse scattering transform has its roots in the study of water waves. The broad implications for researchers in fluids are that a solid grounding in the tools of applied mathematics are highly recommended, if not essential.

   
Preliminary and Foundational Courses
MATH 400: Partial Differential Equations
MATH 401: Green Functions and Variational Methods
MATH 450/550: Perturbation Methods
MATH 521: Numerical Analysis of PDEs
MATH 552: Dynamical Systems Theory
CHBE 557: Fluid Mechanics
MATH 607E: Numerical Methods for Differential Equations

Fluids Courses
EOSC 512: Geophysical Fluid Dynamics
MATH 519: Hydrodynamic Stability
MATH 557: Linear and Nonlinear Waves
MATH 606: Mathematical Modelling of Complex Fluids

Further Options
MECH 510: Computational Methods in Transport Phenomena
MATH 551: Asymptotic Analysis for PDEs
MATH 554: Symmetries and Differential Equations
MATH 556: Industrial Mathematical Modelling
 
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Sample Publications

Listed below are some of the recent theses and journal publications by IAM students, IAM faculty and IAM postdoctoral fellows in the field of Fluid Mechanics. Click on the item of interest to open a thesis file, an article pdf on the author's web page, or an article abstract on the journal site.

 
Chunfeng Zhou, Pengtao Yue and Jimmy Feng. Dynamic Simulation of Capillary Breakup of Nematic Fibers: Molecular Orientation and Interfacial Rupture. Journal of Computational and Theoretical Nanoscience, 7, pp. 683-692 (2010).

Anirban Guha and Ian Frigaard. On the Stability of Plane Couette-Poiseuille Flow with Uniform Crossflow. Journal of Fluid Mechanics, 656, pp. 417-447, (2010).

Ian Chan. Parametric Subharmonic Instability and the β-Effect. M.Sc. Thesis, University of British Columbia (2010).

Neil Balmforth, Dan Coombs, and Sydney Pachmann. Microelastohydrodynamics of Swimming Organisms near Solid Boundaries in Complex Fluids. Quarterly Journal of Mechanics and Applied Mathematics, 63(3), pp. 267-294 (2010).

Christian Schoof and R. C. A. Hindmarsh. Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models. Quarterly Journal of Mechanics and Applied Mathematics, 63(1), pp. 73-114 (2010).

Christian Schoof. Coulomb Friction and Other Sliding Laws in a Higher-Order Glacier Flow Model. Mathematical Models and Methods in Applied Sciences, 20(1), pp. 157-189 (2010).

Maria Khomenko. Viscous Fluid Instabilities Under an Elastic Sheet. M.Sc. Thesis, University of British Columbia (2010).

S. S. Li and Greg Lawrence. Unsteady Two-layer Hydraulic Exchange Flows with Friction. Journal of Fluid Mechanics, 633, pp. 99-114 (2009).

Peng Gao and Jimmy Feng. Enhanced Slip on a Patterned Substrate Due to Depinning of Contact Line. Physics of Fluids 21, 102102 (2009).

Andreas Putz, Ian Frigaard, and Mark Martinez. On the Lubrication Paradox and the Use of Regularisation Methods for Lubrication Flows. Journal of Non-Newtonian Fluid Mechanics, 163, pp. 62-77 (2009).

Eric DeGiuli. Turbulent Flow in Geophysical Channels. M.Sc. Thesis, University of British Columbia (2009).

Diwen Zhou, Pengtao Yue and Jimmy Feng. Viscoelastic Effects on Drop Deformation in a Converging Pipe Flow. Journal of Rheology, 52, pp. 469-487 (2008).

Andreas Putz, T. Burgehla, Ian Frigaard, and Mark Martinez. Settling of an Isolated Spherical Particle in a Yield Stress Fluid. Physics of Fluids (2008).

Sydney Pachmann. Swimming in Slime. M.Sc. Thesis, University of British Columbia (2008).

Neil Balmforth, Shilpa Ghadge, Atichart Kettapun, and Shreyas Mandre. Bounds on Double-Diffusive Convection. Journal of Fluid Mechanics, 569, pp. 29-50 (2006).

Shreyas Mandre. Two Studies in Hydrodynamic Stability. Ph.D. Thesis, University of British Columbia (2006).
 
   
Defect formulation of stratified Kolmogorov flow: Kelvin-Helmholtz instability (left), Holmboe instability (centre), and Taylor-Caulfield instability (right)
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Last Update: 23 Nov 2010 UBC Institute of Applied Mathematics © 2010 All rights reserved.