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3.5 Giant cells, waves, and solar subsurface weather

Differential rotation and meridional circulation are essential components of solar interior dynamics but it is also of fundamental importance to investigate the large-scale convective motions which maintain them and which, therefore, lie at the root of solar variability (Section 1). There is no doubt that large-scale structure (l < 100) is present in surface velocity maps obtained from Doppler measurements, feature tracking, and local helioseismology (e.g., Stix, 2002Jump To The Next Citation Point). However, it has been notoriously difficult to identify characteristic patterns or to obtain quantitative diagnostics of large-scale convective motions.

The convection power spectrum in the photosphere obtained from Doppler measurements peaks at granulation scales (l > 1000), with a secondary peak at l ~ 120, corresponding to supergranulation (Hathaway, 1996bHathaway et al., 2000). At lower wavenumbers, the velocity spectrum appears to drop off nearly linearly: v(l) ~ l.

View Image

Figure 3: Shown is a synoptic horizontal flow map 10.2 Mm below the photosphere inferred from ring diagram analysis (Haber et al., 2002Jump To The Next Citation PointHindman et al., 2004Jump To The Next Citation Point). Vectors indicate flow speed and direction while the underlying image represents the radial magnetic field strength (red and green denote opposite polarity). Characteristic velocity amplitudes are -1 30 m s. These inversions are based on MDI data averaged over 7 days and sampled over square horizontal patches, each spanning 15o in latitude and longitude. The data shown have not been corrected for inclination (p-angle) effects which would shift velocities by about 4 m s-1 (courtesy D. Haber).
Recently, several groups have reported long-lived features in Dopplergrams which are highly correlated in longitude, corresponding to azimuthal wavenumbers of m = 0- 8 (angular extent o > 45) but with a narrow latitudinal extent of not more than about 6o (Ulrich, 19932001Jump To The Next Citation PointBeck et al., 1998Jump To The Next Citation Point). Although Beck et al. (1998) interpret these features as giant convection cells, Ulrich (2001Jump To The Next Citation Point) argues that they more likely comprise a spectrum of inertial oscillations, possibly related to Rossby wave modes (Appendix A.6) and perhaps also to torsional oscillations (Section 3.3).

Evidence for a dramatically different giant cell structure has been presented by Lisle et al. (2004Jump To The Next Citation Point). They study the supergranulation pattern using correlation tracking and find a tendency for north-south alignment of supergranular cells. Such an alignment would be expected if the supergranulation were advected by larger-scale, latitudinally-elongated lanes of horizontal convergence such as those commonly seen in numerical simulations of solar convection (Section 6.2). Advection by such structures may also help to explain why the supergranulation pattern appears to rotate faster than the surrounding plasma (Lisle et al., 2004).

The most substantial recent advance in the search for large-scale non-axisymmetric motions in the solar envelope has been the mapping of horizontal flows by local helioseismology, as shown in Figure 3View Image. After subtracting out the contributions from differential rotation and meridional circulation, the residual flow maps reveal intricate, evolving flows on a range of spatial scales (Haber et al., 2002Jump To The Next Citation PointZhao and Kosovichev, 2004Jump To The Next Citation PointKomm et al., 2004Jump To The Next Citation PointHindman et al., 2004). Such flow patterns have become known as solar subsurface weather, SSW (Toomre, 2002).

The inferred SSW patterns show a high correlation with magnetic activity, becoming more complex at solar maximum. Near the surface, strong horizontal flows converge into active regions and swirl around them, generally in a cyclonic sense (counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere). Deeper down, roughly 10 Mm below the photosphere, the pattern reverses; here flows tend to diverge away from active regions (Zhao and Kosovichev, 2004Jump To The Next Citation Point).

The distribution and relative amplitude of horizontal divergence and vertical vorticity can provide insight into the nature of the flows and can be used to make contact with theoretical and numerical models. Komm et al. (2004) compute the divergence and vorticity fields from SSW flow maps along with other flow descriptors including the vertical velocity (obtained from the mass continuity equation) and vertical gradients of horizontal flows. The results again show a strong correlation with active regions which are associated with cyclonic vorticity, converging flows, and large velocity gradients.

Other flow diagnostics which can in principle be deduced from SSW flow maps include the horizontal Reynolds stress component < v'hv'f > (see Section 4.3). Although such quantities have not yet been investigated in detail with helioseismic measurements, they have been measured to some degree using sunspots as tracers. The results yield small but generally positive values, indicating equatorward angular momentum transport (Stix, 2002Jump To The Next Citation PointNesme-Ribes et al., 1997).

In addition to giant convective cells, large-scale, non-axisymmetric flow patterns may also arise from wave phenomena. A familiar example is the acoustic wave spectrum which forms the basis of helioseismology. There is also some evidence for the presence of Rossby wave modes or, more generally, inertial oscillations. Ulrich (2001) has interpreted long-lived features in photospheric Dopplergrams as a hierarchy of inertial oscillations with longitudinal wavelengths m < 8. Some hints of these patterns can also be seen in SSW flow maps (Haber et al., 2002). Further evidence for Rossby waves on the Sun has been reported by Kuhn et al. (2000) and Lou (2000). Gizon et al. (2003) have suggested that supergranulation patterns may also exhibit wavelike behavior although this has been disputed by Rast et al. (2004).

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