Peter Bartello

Research interests

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.

November 2012

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