Williams, G. P., 1988: The dynamical range of global circulations - I. Climate Dynamics 2, 205-260.

Abstract: The dynamical range of atmospheric circulations is examined by integrating a global circulation model (GCM) over a wide range of parameter values. We study the influence of rotation rate on moist and dry atmospheres with regular, drag-free, and interior-heated surfaces in Part I, and on axisymmetric, oblique, and diurnally heated moist atmospheres in Part II. Despite their variety, the circulations are composed of only a few elementary forms whose existence, scale, and mix alter as the parameters vary. These elements can be interpreted in terms of standard symmetric-Hadley (SH) and quasi-geostrophic (QG) theories. The natural-Hadley (NH) circulation consists of a polar jet and a hemispheric direct cell, such as occur in slowly rotating SH flows, together with Rossby waves generated by moist convection and barotropic cascades. The quasi-Hadley (QH) circulation consists of a tropical westerly jet and a narrow direct cell, such as occur in the low-latitude part of rapidly rotating SH flows, together with Rossby waves generated by baroclinic instabilities in the neighboring midlatitude part of the SH flows; it occurs only in moist atmospheres. The two QG circulations represent the two extremes of eddy momentum flux produced during eddy cycles - the special form of enstrophy cascade describing nonlinear baroclinically unstable wave growth and barotropic wave dispersion. The QG_gamma element has a latitudinally asymmetric wave dispersion that gives a poleward, jet-traversing momentum transport, while QG_beta has a symmetric wave dispersion that gives a jet-converging momentum transport. Both elements have a westerly jet and three cells. (In Part II, we describe the solstitial symmetric-Hadley, the QG-Hadley, the diurnally modified NH, and the Hadley circulations.) In moist atmospheres, NH circulations exist in the rotational low range (omega* = 0 - 1/4); overlapping QG, and QH elements in the midrange (omega* = 1/2 - 1); and QG_gamma, QG_beta, and QH elements in the high range (omega* = 2-8); here omega* = omega/omega_E is the rotation rate normalized by the terrestrial value. In dry atmospheres, circulations follow a similar progression but have a simpler blend because they lack a QH element. Kinetic energy peaks at omega* = 1/8 in the moist, Hadley-dominated atmospheres but at omega* = 1/2 in the dry, QG-dominated atmospheres. Instability-generated Rossby waves propagate equatorward more easily in the westerlies of the diabatically driven (moist) Hadley cell than in the easterlies of the eddy-induced (dry) direct cell. Temperatures vary from almost barotropic at omega* = 0 to almost radiative-convective at omega* = 8, while maintaining almost constant global means. In modified-surface systems, freeslip conditions eliminate the QH element from a moist atmosphere and allow strong deep easterlies to arise in low latitudes to balance the strongly barotropic westerly jets that occur in midlatitudes. In a regular dry atmosphere, enhanced surface heating in low latitudes imitates latent heating and produces a tropical circulation resembling that of the moist QH element. Overall, circulation theory works well in explaining the GCM states but does not, as yet, describe the interactions among elements or reveal how jet scales are determined, nor explain phenomena at the extremes of the parameter range.