7.6 Models and rotation in the convection zone

The interior rotation is only one part of the complex system that drives the solar cycle, but it is perhaps still the easiest part to measure in the solar interior; the meridional circulation can be directly measured only in the shallower subsurface layers, and buried magnetic fields can at best only be inferred indirectly. The differential rotation in the convection zone must arise from the interaction of convection cells and Coriolis forces, with the meridional motions playing an important part.

Early depictions of the solar dynamo (see, for example, Köhler 1974Durney 1975) required a rotation rate increasing inward, and a meridional flow rising at the poles and sinking at the equator, in order to drive the solar cycle migration of the activity belts in the observed sense. This picture, taken together with rotation on cylinders, would have meant that the observed surface differential rotation was a superficial phenomenon, with the dynamo operating in the unobservable deeper layers. At this stage, there does not seem to have been a clear distinction made between the direction of the meridional circulation at the surface and the direction of migration of the magnetic activity belts during the solar cycle, which are of course now understood to operate in opposite directions; the poleward meridional flow at the surface was first measured by Duvall Jr (1979).

The models of Glatzmaier (1985) and Gilman and Miller (1986Jump To The Next Citation Point), which were among the first numerical simulations of solar rotation and the dynamo, have been cited, for example by Wilson (1992Jump To The Next Citation Point) as dating from “Prior to the advent of helioseismology,” but this is not quite correct. In fact, both these papers refer to the Duvall and Harvey data, and Gilman and Miller (1986Jump To The Next Citation Point) also mentions the observations of Brown (1985), suggesting that the model results could be consistent with the helioseismic observations if there were a layer of inward-increasing velocity below the surface and above the domain of the simulation. The simulations in both cases, like their precursors over the previous several years such as that described by Gilman and Miller (1981), produced rotation approximately constant on cylinders and increasing outward, which would result in a dynamo wave propagating poleward if the dynamo were operating in the bulk of the convection zone. The main message that modelers in the late 1980s seem to have taken from the observations was that the rotation rate was increasing outward, in agreement with the simulations of Gilman and Miller (1986Jump To The Next Citation Point) but in disagreement with the α-effect dynamo picture, which required a rotation rate increasing inward; see Parker (1987) for a review representing a theorist’s perspective on the state of play at this stage. This led Gilman and Miller (1986) to suggest (not for the first time; see also, for example, Galloway and Weiss 1981) that the dynamo might be operating in a thin layer at the bottom of the convection zone; this speculation was further reinforced by the later helioseismic inferences that clearly showed this shear layer, or tachocline (see Section 6) and the approximately radial configuration of the rotation in the convection zone.

Even quite recent global simulations of convection (Brun et al., 2004Jump To The Next Citation Point, for example, ) still show some tendency towards rotation on cylinders, but the higher-resolution calculation of Miesch et al. (2008Jump To The Next Citation Point) mostly eliminates the cylindrical effect and produces a rotation pattern, based on giant convection cells, that after suitable temporal averaging looks quite solar-like, as illustrated in Figure 21View Image.

View Image

Figure 21: Three temporally averaged rotation profiles from the spherical-shell simulations of (a) Brun et al. (2004), (b) Browning et al. (2006), and (c) Miesch et al. (2008) (reproduced by permission of the AAS).

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