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1. Introduction

Crucial to our understanding of chemical and radiative properties of the middle atmosphere is an understanding of the mean meridional circulation and its dynamical and radiative causes. By mean meridional circulation we mean a zonally averaged, long-term, systematic motion of air parcels. This circulation plays an important role in carrying chemical species away from source regions, as well as creating significant departures from local thermodynamic equilibrium. See, eg., WMO (1985), Andrews et al. (1987) and a recent review in WMO (1999).

Because of the angular momentum structure of the atmosphere, dominated by the contribution from the Earth's axial rotation, a mean meridional velocity at a particular extratropical location cannot persist without a systematic zonal momentum force acting at the same location. This force is required for parcels of air to cross the nearly vertical isosurfaces of angular momentum. Such effects have been recognized since the works of Dickinson (1968,1969), and discussed more recently in Held & Hou (1980), and Haynes et al. (1991). The latter derived an expression for the zonally symmetric, steady state vertical velocity, which, under time-periodic conditions, can be extended to

Here denotes an annual average, the primes denote the time varying component, is the Jacobian determinant, and the integral is along a contour of constant angular momentum. Thus, the force has a ``downward control'' on the meridional circulation.

Despite a good understanding of the mechanisms involved in driving the observed mean meridional circulation in the extratropics, we still do not have a clear idea of those involved at low latitudes, where contours of angular momentum deviate significantly from the vertical, and where the dynamical link between the zonal mean velocity and temperature fields is weaker. In particular there is still no complete explanation of the non-zero time-averaged upward motion observed in low latitudes in the lower stratosphere (hereafter ``tropical upwelling'') Some progress has been made recently by Plumb & Eluszkiewicz (1999), who concluded that the mean meridional circulation was predominantly linear even at low latitudes and that artificial viscosity was ultimately responsible for the tropical upwelling that they obtained in an idealized model. In the present work we examine the relative importance to tropical upwelling of several different effects, namely the seasonal cycle (transience), nonlinearity, and low latitude diffusive type forces (whether real or artificial). While we agree with Plumb & Eluszkiewicz (1999) that the tropical upwelling response has some linear dependence, we show that nonlinear effects nevertheless play an important role.

The outline of the work is as follows. In Section 2, we give a brief description of the model and diagnostics used later, followed by an example of a meridional circulation obtained with a model in which waves are included explicitly. We consider both seasonally varying and steady state calculations. In Section 3, we compare the results of Section 2 with the circulation obtained by forcing a zonally symmetric model with the zonal momentum force obtained from the wave-one model. In Section 4, we consider an idealization of the form of the wave forcing to investigate in more detail the importance of nonlinearity, diffusion, and transience. In section 5, we give a short summary of the main results.