Graduate student and post-doctoral opportunities in fluid mechanics/oceanography/physical limnology/nonlinear waves

My research offers possibilities for students with a variety of interests including very theoretically minded students, including those with interests on the Pure Mathematics side of the Applied Math spectrum, numerically/computationally oriented students and students with very applied scientific interests. Work can involve developing new theoretical models and/or numerical models, running large computational fluid dynamics models to address scientific questions, data analysis and the interpretion of numerical model results with physical/mathematical models. Some sample projects are listed below.

In addition to the specific projects listed below I am interested in supervising students with interests in any aspect of nonlinear waves, such as nonlinear optics. In the realm of fluid mechanics I also have general interests in stratified flows, large scale physical oceanography (e.g., eddies) and ocean acoustics (in particular, acoustic transmission through internal wave fields). If you have an interest in one of these areas or others in fluid mechanics, and you are interested in pursuing graduate studies in the Department of Applied Mathematics at the University of Waterloo please get in touch by

1. Parametrizations of high-frequency, non-hydrostatic internal waves for use in hydrostatic models.

   Hydrostatic models are appropriate for modelling phenomena whose horizontal length scale is long compared with the vertical length scale. The use of the hydrostatic approximation is popular because it simplifies numerical models resulting in much shorter model run times. Hydrostatic models cannot, however, model internal solitary waves and other high-frequency waves. There are different aspects of this work that would appeal to a variety of students: some very theoretical (e.g., working with nonlinear wave equations) and some very numerical. Funded by CFCAS.

2. Hydrodynamic Instability

   Theoretical and computational problems related to shear instabilities and mixing associated with tidal flow over a sill and in large amplitude internal solitary waves.

3. Stochastic modelling of nonlinear internal waves.

   Internal waves play a fundamental role in transferring energy from large scale to small dissipation scales in the oceans, atmosphere and lakes. Because of the enhanced mixing that occurs as small scale internal waves break, this nonlinear process has implications ranging from effecting large scale circulation in the ocean (and hence climate) to nutrient fluxes. Should appeal to the more theoretically inclined student.

4. Nonlinear waves.

   Including surface wave problems involving Hamiltonians and Lie Transforms or nonlinear Fourier analysis. Should appeal to the more theoretically inclined student.

5. Computational Fluid Dynamics (CFD).

   Numerical modelling of complex fluid flows is a necessary part of modern research in fluid dynamics and is one that I have had a long-time interest in. Most of the animations animations you can view on my web site were created from simulations done with a 2-D CFD code that I developed. A 3-D spectral code is currently under development in our group. In collaboration with my colleague Marek Stastna I am planning to develop an unstructured finite volume/finite element lake model for studying processes in lakes with complex geometries. There are many opportunities for students with interests in the area of CFD.

More details of my research interests are provided here. Research interests of other faculty in the Environmental and Geophysical Fluid Dynamics Group can be found on their web pages.

Both Canadian and international students are encouraged to apply. All accepted students will be provided with sufficient funding to cover tuition and living expenses.

Last modified: October 31, 2007