# 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.