Thermally Driven Tropical Circulations under Rayleigh Friction and Newtonian Cooling: Analytic Solutions*

In this paper, the atmospheric circulations on an equatorial beta plane in response to steady tropical heating are investigated by analytically solving a set of linear equations. Special emphasis is placed on the horizontal structure of forced response under the different combinations of momentum damping and thermal damping, as well as the effect of the zonal domain on the forced responses. Two zonal domains are considered: a zonally cyclic domain and a zonally unbounded domain. The linear model is decomposed in terms of the vertical eigenfunctions in a vertically semi-infinite domain. A new feature of the solution is the existence of a continuous spectrum corresponding to energy propagation out the top of the troposphere. The resulting shallow-water equations are then solved using a method similar to that of Gill. Since the zonal decay scale is proportional to the inverse of the square root of the product of the Rayleigh friction rate and the Newtonian cooling rate, the solutions in a zonally un...