Hadley cell emergence and extent in axisymmetric, nearly inviscid, planetary atmospheres

Abstract

The authors consider constraints from axisymmetric, nearly inviscid theory on Hadley cell emergence and extent in dry planetary atmospheres. Existing versions of the well-known Hide's constraint relating Hadley cell emergence to the distributions of absolute angular momentum (M) and the vertical component of absolute vorticity (η) are unified, amounting to any of M > Ωa^2, M < 0, or fη < 0 occurring at any latitude. The M < 0 condition coincides with the gradient-balanced zonal wind in radiative convective equilibrium (RCE; u_(rce)) becoming non-real valued. The resulting angular momentum conserving (AMC) circulation must span all latitudes where any of these conditions are met or where u_(rce) exceeds the AMC zonal wind (u_(amc)) corresponding to planetary angular momentum at the latitude of the circulation's ascent branch (φ_a), but a generally valid prognostic theory for φa remains elusive. Nevertheless, given a diagnosed φ_a, the u_(rce) > u_(amc) condition provides a simple explanation for why cross-equatorial Hadley circulations typically extend as far into the winter- as the summer hemisphere. The classical "equal-area" models predict φ_a but typically must be solved numerically and always predict φ)a at or poleward of the RCE forcing maximum (φ_m) for φ_m ≠ 0. In an idealized dry general circulation model, a pole-to-pole cross-equatorial Hadley cell emerges if the corresponding RCE state meets some combination of these extent criteria over the entire summer hemisphere. Conversely, the cell edge and φ_a sit far equatorward of φ_m if those criteria are not satisfied near φ_m.