The Linear Response of a Global Atmosphere to Tropical Heating

Effect of Planetary Rotation

Abstract

We study the basic features of linear stationary response of a global atmosphere to tropical heating in connection with effects of planetary rotation. For this purpose, with the linearized shallow water equations on a sphere, we calculate the horizontal structure of circulations for a wide range of the parameter ε(0_??_ε_??_10000), the square of the ratio of the rotational velocity of the planet to the velcoity of the gravity wave.
First, we examine responses to tropical heating which is concentrated in an area of finite extent and symmetric about the equator. When ε is small, the induced circulation is simply a direct circulation. An increase of ε makes the circulation confined to the equatorial region and intensifies the westerly inflow in the west of the heating region. The origin of the east-west asymmetry in the circulation is discussed in the light of vorticity balance. For ε_??_100, the circulation is mainly composed of Kelvin and Rossby waves. Gill's solution (1980) obtained in the simplified model is similar to ours for ε=100 or 1000.
Second, the case that the tropical heating is antisymmetric about the equator is examined. For small ε a direct flow crossing the equator predominates. When ε becomes large, the flow meanders in the west of the heating region. For ε=10000, the flow crossing the equator becomes negligible and the two closed circulations are formed separately in each hemisphere.
For ε=10, we calculate circulations for some values of Rayleigh friction and Newtonian cooling rate; the results are sensitive to this value. We discuss the effects of dissipation processes on steady balance in the light of equations of motion and thermodynamics.
We examine also the response to heating which is spread over the sphere.