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Astron. Astrophys. 364, 876-878 (2000)

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4. The turbulent region in the Sun

Let us now examine where the instability condition (7) is fulfilled is the Sun. According to (1), the maximum shear rate at the top of the solar radiation zone amounts to

[EQUATION]

as illustrated in Fig. 1.

[FIGURE] Fig. 1. The shear rate [FORMULA] with respect to radius beneath the convection zone for the colatitudes [FORMULA] (full), [FORMULA] (dashed) and [FORMULA] (dash-dot-dash).

It is convenient to introduce the non-dimensioned parameter

[EQUATION]

according to Eq. (7), the turbulent shear instability will occur if:

[EQUATION]

Note that [FORMULA], the ratio of Reynolds and Richardson critical numbers, is rather uncertain, in particular because [FORMULA] depends on the vertical flow profile.

We have calculated [FORMULA] as a function of radius and colatitude in the radiative zone beneath the tachocline of a standard solar model, in order to delimit the regions where the turbulent instability is established.

The standard solar model is computed with CESAM code (Morel 1997); the evolution includes the pre main-sequence phase. Basically, the physics and calibration parameters are the same as in Morel et al. (2000); it uses OPAL opacities and equation of state, the microscopic diffusion coefficients of Michaud & Proffitt (1993) and the recently updated thermonuclear reaction rates of the European compilation NACRE (Angulo et al. 1999). The angular velocity beneath the convection zone is derived from Eq. 1. The dynamical viscosity is taken as in a fully ionized hydrogen plasma.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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