Idealized annually averaged Macroturbulent Hadley Circulation in a Shallow Water Model

The interaction of midlatitude eddies and the thermally driven Hadley circulation is studied using an idealized shallow water model on the rotating sphere. The contributions of the annually averaged differential heating, vertical advection of momentum from a stationary boundary layer, and the gross effect of eddies, parameterized by Rayleigh damping, including a hemispherically asymmetric damping, are examined at steady state. We find that the relative dominance of eddies, as quantified by the local Rossby number, is predicted by an effective macroturbulent Hadley circulation Prandtl number, Pr. In addition, viscous solutions of the Hadley circulation width and strength, subtropical jet amplitude and equator to pole temperature difference, scale as deviations from the respective inviscid solutions. Semi-analytic solutions for the steady circulation are derived in the limit of weak eddy-dominance (small Pr) as deviations from the respective inviscid solutions. These solutions follow a 3-region paradigm: weak temperature gradient at the ascending branch of the Hadley circulation, monotonically decreasing angular momentum at the descending branch, and modified radiative-convective equilibrium at extratropics. Using the 3-region solutions, scaling relations found in the full solutions are reproduced analytically. The weak eddy-dominance solutions diverge from the full solutions as Pr increases and may become invalid for Pr > 1 due to the breakdown of the 3-region global circulation structure. The qualitative predictions of the response of the Hadley circulation to heating based on the weak eddy-dominance solutions and Pr are in agreement with the findings of more complex models and the observed atmosphere.