Williams, Gareth P. 1988. The dynamical range of global circulations - II. Climate Dynamics, 3, 45-84.

Abstract: The dynamical range of global atmospheric circulations is extended to specialized parameter regions by evaluating the influence of the rotation rate (omega) on axisymmetric, oblique, and diurnally heated moist models. In Part I, we derived the basic range of circulations by altering omega for moist and dry atmospheres with regular and modified surfaces. Again we find the circulations to be composed of only a few elementary forms. In axisymmetric atmospheres, the circulations consist of a single jet in the rotational midrange (omega* = 1/2-1) and of double jets in the high range (omega* = 2-4), together with one or two pairs of Hadley and Ferrel cells; where omega* = omega/omega_E is the rotation rate normalized by the terrestrial value. These circulations differ from those predicted by first-order symmetric-Hadley (SH₁) theory because the moist inviscid atmosphere allows a greater nonlinearity and prefers a higher-order meridional mode. The axisymmetric circulations do, however, resemble the mean flows of the natural system - but only in low latitudes, where they underlie the quasi-Hadley (QH) element of the MOIST flows. In midlatitudes, the axisymmetric jets are stronger than the natural jets but can be reduced to them by barotropic and baroclinic instabilities. Oblique atmospheres with moderate to high tilts (theta = 25° - 90°) have the equator-straddling Hadley cell and the four basic zonal winds predicted by the geometric theory for the solstitial-symmetric-Hadley (SSH) state: an easterly jet and a westerly tradewind in the summer hemisphere, and a westerly jet and an easterly tradewind in the winter hemisphere. The nonlinear baroclinic instability of the winter westerly produces a Ferrel cell and the same eddy fluxes as the quasi-geostrophic QG_gamma element, while the instability of the summer easterly jet produces a QG-Hadley (QGH) element with a unique, vertically bimodal eddy momentum flux. At high theta and low omega*, the oblique atmospheres reach a limiting state having global easterlies, a pole-to-pole Hadley cell, and a warm winter pole. At low tilts (theta < 10°), the oblique circulations have a mix of solstitial and equinoctial features. Diurnal heating variations exert a fundamental influence on the natural-Hadley (NH) circulations of slowly rotating systems, especially in the singular range where the zonal winds approach extinction. The diurnality just modifies the NH element in the upper singular range (1/45 < omega* < 1/16 ), but completely transforms it into a subsolar-antisolar Halley circulation in the lower singular range (0 < omega* < 1/45). In the modified NH flows, the diurnality acts through the convection to enhance the generation of the momentum-transferring planetary waves and, thereby, changes the narrow polar jets of the non-diurnal states into broad, super-rotating currents. Circulation theory for these specialized flows remains rudimentary. It does not explain fully how the double jets and the multiple cells arise in the axisymmetric atmospheres, how the QGH element forms in the oblique atmospheres, or how waves propagate in the slowly rotating diurnal atmospheres. But eventually all theories could, in principle, be compared against planetary observation: with Mars testing the QGH elements; Jupiter, the high-range elements; Titan, the equinoctial and solstitial axisymmetric states; and Venus, the diurnally modified NH flows.