Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves

Motions on planetary spatial scales in the atmosphere are governed by
the planetary geostrophic equations. However, not much attention has
been paid to the interaction between the baroclinic and barotropic
flow within the planetary geostrophic scaling. This is the focus of
the present study by utilizing planetary geostrophic equations for a
Boussinesq fluid supplemented by an asymptotically derived evolution
equation for the barotropic flow. The latter is effected by meridional
momentum flux due to baroclinic flow and drag by the surface wind. The
barotropic wind on the other hand affects the baroclinic flow through
buoyancy advection. By relaxing towards a prescribed buoyancy profile
the model produces realistic major features of the zonally symmetric
wind and temperature fields. We show that there is considerable
cancelation between the barotropic and the baroclinic surface zonal
mean zonal wind. The linear and nonlinear model response to steady
diabatic zonally asymmetric forcing is investigated. The arising
stationary waves are interpreted in terms of analytical solutions. We
also study the problem of baroclinic instability on the sphere within
the present model.

Reference: Dolaptchiev, S. I., Achatz, U. and Th. Reitz, 2019: Planetary
geostrophic Boussinesq dynamics: barotropic flow, baroclinic
instability and forced stationary waves, Quart. J. Roy. Met. Soc., 145: 3751-3765.