My research employs both theoretical and numerical techniques to study
fluid turbulence in the atmosphere and oceans. A major recent thrust
has been the study of the statistical nature of the flow as a function
of rotation and stratification. The simplifying assumptions employed at
larger scales, that rotation and stratification terms in the governing
equations are predominant and approximately balanced by other terms,
become invalid at smaller scales. The interactions between large-scale
vortices and more general turbulent and wave motions are therefore the
subject of these studies, as is the effect on the turbulent transport
of passive scalars such as pollutants or ozone. A simple example is
whether turbulent motions preferentially send energy downscale (as in a
breaking wave at the shore) or upscale (as in the merging of two eddies
to make a larger one). Both are known to occur, depending on the
relative strengths of rotation and stratification. Both must be
accounted ! for in coarse-resolution models, such as the ones used for
weather and climate studies, but clearly in a different way.
In the large-scale limit wave motion is dissipated via downscale
transfer to molecular scales. In this environment attention is
naturally directed to the vortices, as they dominate the flow. They
have often been considered as isolated, both from each other and from
the rest of the motion. However, a recent examination of large-scale
turbulence without waves (2D turbulence) was able to formalize the
separation between isolated eddies and a low-level background of
vorticity filaments. It remains to be seen whether these results extend
to more complete models of geophysical flows.
Since there is a reliance on numerical simulation, research on the
numerics is undertaken in parallel. At the expense of accuracy, weather
and climate models are forced to use numerical methods that allow for
an enormous reduction in the true range of time and length scales.
Minimizing the numerical damage as a function of flow statistics is
another research priority.
I am also involved with the Applied Math group in the Department of
Mathematics and Statistics as well as the McGill seminar series in
Computational Science and Engineering.