Sack Lunch Seminar (SLS)

A "Vortex in Cell" Model for Quasi-Geostrophic, Shallow Water Dynamics on the Sphere





The vortex in cell (VIC) method has been found to be an attractive computational
choice for solving a number of fluid dynamical problems. The Lagrangian advection
of particles leads to stability of the method even for long time steps. Moreover,
conservation of particle properties, such as potential vorticity, can be enshrined
at the heart of the numerical procedure. In this paper we describe a numerical
implementation of the VIC method for a reduced gravity, quasi-geostrophic model
and make use its novel aspects to explore the interaction of waves and turbulence
on the sphere. The Lagrangian advection of particles is performed using a fourth
order Runge-Kutta method and the stream-function is obtained by the inversion
of potential vorticity over an underlying Eulerian grid. The scheme is tested in the
simulation of Rossby and Rossby-Haurwitz waves. Encouraging results are obtained
for various radii of deformations corresponding to both the atmosphere and ocean.