Horizontal Coupling of Rotation

In models without magnetic field, the horizontal turbulence enforces an almost constant rotation on isobars, which makes shellular rotation (Sect. 12.1). It is likely that a strong azimuthal field reduces or even suppresses the horizontal turbulence. We define a horizontal diffusion or viscosity coefficient due to the magnetic field as the square of the typical length scale r divided by the typical timescale of the magnetic instability, i.e., ob 1 as given by (13.61),

DBh = r2 Ob = r2 K/Q) = —, for Q >> (Oa . (13.98) h 4npQ

The interaction of turbulence and magnetic field is complex. We suggest, as a first guess, that if DBh > Dh the magnetic coupling dominates over horizontal turbulence and reciprocally. The value of DBh is larger than 1011 cm2 s-1 in a 15 MQ model with an initial rotation of 300 km s-1. This is equal or larger than the coefficient of horizontal turbulence (Sect. 12.2). Thus, magnetic field may dominate over the horizontal turbulence. The value of DBh is large enough to ensure horizontal coupling, so that the assumption of shellular rotation is still valid.

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