Horizontal energy propagation in a baroclinic atmosphere with meridional and zonal structure

A baroclinic model was developed. The model is linear, steady state, baroclinic (2 level) and based on the primitive equations. The unique features of the model are: (1) The basic state u and T fields are functions of wavelength, theta, and rho, (2) A mean meridional circulation v, w, which may be a function of wavelength, theta, and rho, and p may be included, (3) Dissipation may be a function of theta, wavelength, rho, p (e.g., differ over land and sea). Because the basic state is a function of longitude, the equations are not separable in wavelength and the usual semi-spectral solution procedure is not applicable. The model solutions can be found in a straight forward (brute force) way by discretizing the model equations directly on a wavelength, theta, rho, p grid. There are six dependent (perturbation) variables: u, v, and geopotential at levels 1 and 2. The thermal forcing is prescribed at the intermediate vertical level. The linearized equations may be written.