# Deep and Shallow Overturning Circulations in the Tropical Atmosphere

September 27, 2013

Gabriela Mora-Rojas

*Hosted by* Wayne Schubert (advisor), Mark DeMaria, Eric Maloney, Thomas Birner, Craig Trumbo (Journalism and Technical Communication)

## Abstract

This dissertation examines the dynamics of zonally symmetric, deep and shallow overturning circulations in the tropical atmosphere. The dynamics are discussed in the context of idealized analytical solutions of the equatorial β-plane version of the Eliassen meridional circulation equation that arises in balanced models of the Hadley circulation. This Elliptic equation for the meridional circulation has been solved analytically by first performing a vertical normal mode transform that converts the partial differential equation into a system of ordinary differential equations for the meridional structures of all the vertical modes. These meridional structure equations can be solved via the Greenâ€™s function, which can be expressed in terms of parabolic cylinder functions of half-integer order. The analytical solutions take simple forms in two special cases: (1) Forcing by deep diabatic heating that projects only onto the first internal mode in the absence of Ekman pumping; (2) Forcing by Ekman pumping in the absence of any diabatic heating. Case (1) leads to deep overturning circulations, while case (2) leads to shallow overturning circulations. Both circulations show a marked asymmetry between the winter hemisphere and summer hemisphere overturning cells. This asymmetry is due to the basic anisotropy introduced by the spatially varying inertial stability coefficient in the Eliassen meridional circulation equation. A simple physical interpretation is that fluid parcels forced near the equator to overturn by diabatic and frictional processes tend to move much more easily in the horizontal direction because the resistance to horizontal motion (i.e. inertial stability) is so much less than the resistance to vertical motion (i.e., static stability).