Combining Thermodynamic and Dynamic Perspectives of Tropical Circulation to Constrain the Downdraft Width of the Hadley Cell

Abstract

In the Hadley circulation downdraft, to leading order vertical potential temperature advection balances the "effective" heating, comprising the sum of diabatic heating and eddy heat flux divergence, placing a thermodynamic constraint on vertical velocity. Insofar as downdraft-averaged effective heating and static stability do not vary with planetary parameters, neither can vertical velocity --- an "omega governor." Separately, in the eddy-driven (i.e. small-Rossby-number) limit, extratropical eddy stresses also constrain the cell strength dynamically. We combine these thermodynamic and dynamic mechanisms to derive new and identical scalings for the downdraft width and overturning strength with rotation rate. With the omega governor maintaining fixed vertical velocity, the downdraft must narrow or widen in order to attain the overturning strength dictated by the eddy stresses. We evaluate the validity of this new scaling using model simulations over a broad range of rotation rates and model forcing schemes.