In this paper, the atmospheric circulations on an equatorial beta-plane in responseto steady tropical heating are investigated by analytically solving a set of linearequations. Special emphasis is placed on the horizontal structure of forced responseunder the different combinations of momentum damping and thermal damping, as well asthe effect of the zonal domain on the forced responses. Two zonal domains areconsidered: a zonally cyclic domain and a zonally unbounded domain.
The linear model is decomposed in terms of the vertical eigenfunctions in avertically semi-bounded domain. The resulted shallow water equations are then solvedusing a method similar to that in Gill (1980).
Our results show that the zonal decay scale is proportional to the inverse of thesquare root of the product of Rayleigh friction rate and Newtonian cooling rate. Hence, the solutions in a zonally unbounded domain can be good approximations for the solutions in a zonally cyclic domain only when both Rayleigh friction and Newtonian cooling are strong enough. The characteristic meridional scale of the shallow water system under different types of damping is the effective equatorial radius of deformation, which is the equatorial radius of deformation of the shallow water system multiplied by the fourth root of the Prandtl number.
In both the Rayleigh-friction-dominant case and the Newtonian-cooling-dominant case,the solutions are essentially uniform in a zonally cyclic domain except in a verynarrow zone along the Equator. However, since the characteristic meridional scale isvery large for the Rayleigh-friction-dominant case, the forced response can extendfar outside the heating latitude. Contrast to that, in the Newtonian-cooling-dominantcase, the characteristic meridional scale is very small and the forced response isconfined to the heating latitudes.
The implications of these solutions are also discussed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics