I describe the domain as a "pizza box" because it is a shallow box. Two simulations are shown: a low-resolution simulation with 41×41×11 grid points and a high-resolution simulation with 161×161×21 grid points.

In distance, it is much more shallow: 2000×2000×1. So we can think of the domain as a box 20,000 km on a side and 10 km deep, draped over the north pole ... but we keep the geometry Cartesian ... an f-plane.

• Computation is with Python and numpy.
• In the simulations shown here, the Rossby radius of deformation is 500.
• The initial state is stably stratified, with the dense fluid gathered toward the center, in thermal wind balance.
• The initial polar vortex is set slightly off-center so that the perturbation is not purely a wave number 4.
• The boundaries are free-slip.
• We initialize with zero thermal wind at the surface, and so put a "jet stream" aloft. The makes all the weather at the surface very quiet, until the baroclinic instability develops.
• The Boussinesq approximation is applied.

Description of the plots

Upper left: horizontal cross-section at the surface

• White contours: pressure anomaly at the surface.
• Color contours: fluid density at the surface.
• Green contours: pressure anomaly at mid-height.
• Black vectors: wind at the surface.

Lower left: vertical cross-section at mid y

• Color contours: fluid density
• Grey contours: wind. dashed: coming at you; solid: going away.

Right: time trace

• red: total kinetic energy in domain
• blue: total potential energy anomaly in domain
• green: sum of red and blue

Hi-res: 161x161x21

If you want to see it: the low-resolution simulation