Axisymmetric Constraints on Cross-Equatorial Hadley Cell Extent

Abstract

We consider the relevance of known constraints from each of Hide's theorem, the angular momentum conserving (AMC) model, and the equal-area model on the extent of cross-equatorial Hadley cells. These theories respectively posit that a Hadley circulation must span: all latitudes where the radiative convective equilibrium (RCE) absolute angular momentum (M_(rce)) satisfies M_(rce) > Ωa^2 or M_(rce) < 0 or where the RCE absolute vorticity (η_(rce)) satisfies f_(ηrce) < 0; all latitudes where the RCE zonal wind exceeds the AMC zonal wind; and over a range such that depth-averaged potential temperature is continuous and that energy is conserved. The AMC model requires knowledge of the ascent latitude φa, which need not equal the RCE forcing maximum latitude φm. Whatever the value of φa, we demonstrate that an AMC cell must extend at least as far into the winter hemisphere as the summer hemisphere. The equal-area model predicts φa, always placing it poleward of φm. As φm is moved poleward (at a given thermal Rossby number), the equal-area predicted Hadley circulation becomes implausibly large, while both φm and φa become increasingly displaced poleward of the minimal cell extent based on Hide's theorem (i.e. of supercritical forcing). In an idealized dry general circulation model, cross-equatorial Hadley cells are generated, some spanning nearly pole-to-pole. All homogenize angular momentum imperfectly, are roughly symmetric in extent about the equator, and appear in extent controlled by the span of supercritical forcing.