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

Abstract

Motions on planetary spatial scales in the atmosphere are governed by the planetary geostrophic equations. However, little attention has been paid to the interaction between the baroclinic and barotropic flows within the planetary geostrophic scaling. This is the focus of the present study, which utilizes planetary geostrophic equations for a Boussinesq fluid supplemented by a novel evolution equation for the barotropic flow. The latter is affected 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. Via a relaxation 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 cancellation between the barotropic and the baroclinic surface zonal mean zonal winds. Linear and nonlinear model responses to steady diabatic zonally asymmetric forcing are investigated, and 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.