We describe an idealized primitive equation model for studying mesoscale
turbulence and leverage a hierarchy of grid resolutions to make
eddy-resolving calculations on the finest grids more affordable. The
model has intermediate complexity, incorporating basin-scale geometry
with idealized Atlantic and Southern oceans, and with non-uniform ocean
depth to allow for mesoscale eddy interactions with topography. The
model is perfectly adiabatic and spans the equator, and thus fills a gap
between quasi-geostrophic models, which cannot span two hemispheres, and
idealized general circulation models, which generally have diabatic
processes and buoyancy forcing. We show that the model solution is
approaching convergence in mean kinetic energy for the ocean mesoscale
processes of interest, and has a rich range of dynamics with circulation
features that emerge only due to resolving mesoscale turbulence.