*Theor. Comp. Fluid Dyn.*, **20**,443-467.

Samuel P. Burns

Department of Applied Physics and Applied Mathematics,
Columbia University, New York, NY.

Adam H. Sobel and Lorenzo M. Polvani

Department of Applied Physics and Applied Mathematics and Department of Earth and Environmental Sciences,
Columbia University, New York, NY.

**Abstract**

A simplified model of the moist axisymmetric Hadley
circulation is examined
in the asymptotic limit in which surface friction is strong
and the meridional wind is weak
compared to the zonal wind.
Our model consists of the Quasi-Equilibrium Tropical Circulation
Model (QTCM) equations on an axisymmetric aquaplanet equatorial beta-plane.
This model includes two vertical momentum modes, one baroclinic
and one barotropic. Prior studies use either continuous stratification,
or a shallow water system best viewed as representing the upper troposphere.
The analysis here focuses on the interaction of the baroclinic and
barotropic modes, and the way in which this interaction allows the
constraints on the circulation known from the fully stratified case
to be satisfied in an approximate way.

The dry equations, with temperature forced by Newtonian relaxation
towards a prescribed radiative equilibrium, are solved
first. At leading order, the resulting circulation has a zonal wind
profile corresponding to uniform angular
momentum at a level near the tropopause, and zero
zonal surface wind, owing to the cancellation of the barotropic and
baroclinic modes there. The weak surface winds are calculated from the
first order corrections. The broad features of these solutions are
similar to those obtained in previous studies of the dry Hadley
circulation. The moist equations are solved next, with a fixed sea surface
temperature at the lower boundary and simple parameterizations of
surface fluxes, deep convection, and radiative transfer. The
solutions yield the structure of the barotropic and baroclinic winds,
as well as the temperature and moisture fields. In addition, we
derive expressions for the width and strength of the equatorial
precipitating region (ITCZ) and the width of the entire Hadley
circulation. The ITCZ width is on the order of a few
degrees in the absence of
any horizontal diffusion and is relatively insensitive to parameter
variations.