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Fluid Mechanics

Fluid flow is governed by complicated nonlinear systems of partial differential equations. In many situations of interest the flow spans a huge range of length scales, with the nonlinearity of the governing equations resulting in the transfer of energy from one length scale to another. Because of this complexity, the field of fluid mechanics has been the birth place of many important ideas in mathematics. It continues to stimulate work in areas such as partial differential equations, asymptotics and perturbation theory, computational methods, and nonlinear waves, including solitons, instability theory, chaos, and stochastic processes.

Research in fluid mechanics spans the spectrum of applied mathematics, and graduate students in this field develop skills in a broad range of areas, including mathematical modelling, analysis, computational mathematics, as well as physical intuition. These skills are interconnected, and hence form a marketable whole for graduating students, because the development of appropriate numerical methods and the set-up and interpretation of numerical simulations hinges on the use of theoretical models of varying complexity, as well as judicious application of the scientific method. Within the field of fluid dynamics there is something for students of all interests, from theoretical problems such as the Clay Institute Millennium Prize for proving existence, uniqueness and regularity for the Navier-Stokes equations to applications in the areas of atmosphere, ocean and climate dynamics, astrophysical problems such as stellar wind dynamics, and the dynamics of shock waves. Research projects range from the development of simple models used to understand aspects of complicated physical processes, to the use of advanced theoretical and numerical methods.

The regular faculty whose primary research area is Fluid Mechanics are:

  • Kevin Lamb (nonlinear waves, internal waves, hydrodynamic instabilities and mixing, computational fluid dynamics, physical oceanography and limnology, coupling of hydrodynamic and bio-geochemical processes in lakes)
  • Francis Poulin (hydrodynamic instabilities, Rossby waves, vortices, physical and biological oceanography)
  • Marek Stastna (internal waves and solitary waves, computational fluid dynamics, bottom boundary layers, porous media, swimming organisms)
  • Michael Waite (turbulence in rotating stratified fluids, vortices, internal waves, mesoscale atmospheric dynamics, moist convection)

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