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Astron. Astrophys. 335, 679-684 (1998)

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4. Results

In the sense of an experiment we start with a Taylor number artificially decreased by 3 orders of magnitude. This can easily be done using large values for [FORMULA]. Then the meridional flow is expected to be small as well as its influence on the differential rotation. The rotation law solution of Küker et al. (1993) is reproduced - close to the empirical knowledge (Fig. 3). The pole is decelerated by about 30% with respect to the equator. The model does not exactly fit the observations deep in the convection zone, i.e. our lower boundary (stress-free) condition is not very realistic (Rüdiger & Kitchatinov 1997). However, the agreement between theory and observation is high in the upper layers of the SCZ. Also the isocontours of the angular velocity given in the bottom line of Fig. 3 comply with the known plots by Libbrecht (1988) and Thompson et al. (1996).

[FIGURE] Fig. 3. The flow pattern in the solar convection zone (SCZ). Here as an experiment the meridional flow is suppressed with an artificially high eddy viscosity: [FORMULA]. TOP LEFT: Normalized meridional flow [FORMULA] at the top (solid) and the bottom (dashed) of the SCZ in units of 10/7 m/s, TOP RIGHT: convection zone rotation law at the equator (solid), in mid-latitudes (45[FORMULA], dotted) and at the poles (dashed). BOTTOM: isoline representations of meridional flow and angular velocity. It is [FORMULA], [FORMULA]

For more realistic values of the parameter [FORMULA] this situation is not preserved (Fig. 4). The meridional flow grows to considerable values (19 m/s) even at the bottom of the SCZ. There it flows towards the equator. The differential rotation at the surface, however, proves to be destroyed. This finding naturally agrees with the content of the `Taylor number puzzle' stressed by Brandenburg et al. (1990).

[FIGURE] Fig. 4. The same as in Fig. 3 but for the viscosity factor [FORMULA] and [FORMULA]

One possible solution of the Taylor number puzzle was presented by Kitchatinov & Rüdiger (1995) using the rotation-induced anisotropy of the thermal eddy conductivity tensor. In the following the question is answered whether the AKA-effect can act in the same direction.

As shown by Fig. 5 the answer is Yes. Without AKA-effect in Fig. 4 the differential rotation is very small and the isolines are of Taylor-Proudman type. With AKA-effect in Fig. 5 the pole-equator difference at the surface and the [FORMULA]-isolines change their shape towards the structure presented in the flow-free case of Fig. 3. The result is that indeed with inclusion of the AKA-effect in our formulation a consistent picture of the solar differential rotation can be formed. The meridional circulation is organized in one dominant cell which in the northern hemisphere flows counterclockwise. While the meridional drift at the surface remains weak, it proves to be much stronger (with values of 15 m/s) at the bottom of the convection zone. There the material flows towards the equator.

[FIGURE] Fig. 5. The same as in Fig. 3 but for [FORMULA], [FORMULA] (maximal value) and the viscosity factor [FORMULA]

However, in Fig. 5 a simplified model for the AKA-effect is used as its [FORMULA]-dependence was ignored. The maximum of the function [FORMULA] ([FORMULA] 0.53) has been used throughout the bulk of the SCZ. If the depth-dependence of the function [FORMULA] (due to our turbulence model) is taken into account, i.e. the AKA-effect is concentrated in the surface layers (cf. Fig. 2), then the differential rotation at the surface is again reduced to 6% with accelerated equator (Fig. 6). The effect is still too small but it goes in the right direction. One can however increase the pole-equator difference to 25 % by increasing the amplitude of [FORMULA] by a factor of only 2. This is due to the appearance of a second cell of meridional circulation with more than 20 m/s. As it flows equatorwards the differential rotation is increased but only for the outer layer of the convection zone.

[FIGURE] Fig. 6. The same as in Fig. 3 but for the viscosity factor [FORMULA] and [FORMULA]

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998