Theoretical Fluid Dynamics

For many years the geophysical fluid dynamics community has been studying the 'slow manifold', which was motivated by understanding the large scale circulation of the atmosphere and has intimate connections to numerical modeling of the weather and climate. The key idea behind a slow manifold is that, for large scales, only the slow dynamics matters and that fast dynamics has only a small impact on the evolution of the dynamics.  These ideas have been discussed in key papers with titles like "On the existence of a slow manifold." "On the nonexistence of a slow manifold," and "The slow manifold -- what is it?"  More recent work shows that the wave part of the dynamics puts energy on and takes energy off of the slow manifold itself, modifying its evolution.

The aim of this project is not to delve into the slow manifold's mathematical existence but instead to ask questions such as: "What is the role of the fast, fast/slow and slow dynamics on the total energy and potential enstrophy? In some systems of equations there is more than one slow manifold. Are these related to one another? Can the energy be shifted from one manifold to another? If so, how?". Then other questions can be asked such as, "How can we use what we know about physics to improve numerical methods such as parallel-in-time methods?" This project can be primarily numerics or physics, or a mixture.

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