baroclinic instability in a pizza box
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
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
The high-resolution simulation.
If you want to see it: the low-resolution simulation