## 3. Basic equationsWe solve the stationary Reynolds equation for a turbulent flow in the inertial reference frame, i.e. The tensor divergence is a vector with the components . denotes the acceleration of gravity which is here assumed uniform. Magnetic fields and deviations from axisymmetry are not considered. Anelastic fluids are only considered, i.e. This adopted, the azimuthal component of (22) is Our energy equation will be very simple. The turbulence is considered to be so intense that the medium is isentropic, i.e. hence there is a direct relation between density and pressure
( is the specific heat). If this is true the
pressure term in (22) can be written as a gradient which disappears
after application of It remains to fix the flow field by For normalization the relations and are used. The density stratification is then represented by . As the conservation law of the angular momentum we get from (24) the dimensionless equation Here also the turbulent fluxes of angular momentum are written in dimensionless form in accord with Eq. (30) is linearized by means of the assumption of mild differential rotation, The meridional Eq. (26) is formulated under the same condition. Hence the `centrifugal force' is reformulated as Here the Taylor number Ta couples the centrifugal terms in (34) to
the contributions of the turbulence-originated Reynolds stress. In
contrast to (31) the latter are normalized with
. The -effect is
normalized with . and at the equator. Like in Küker et al. (1993) we have used the convection zone model by Stix & Skaley (1990) to specify the radial stratification of the parameters. Density and turbulence intensity as well as the mixing-length are taken from the convection zone model. Besides the basic solar rotation rate , the only free parameters are the mixing-length parameter and the factor in the eddy viscosity expression. As an extra parameter to tune the AKA-effect the normalized amplitude has been introduced with as the standard case. © European Southern Observatory (ESO) 1998 Online publication: June 18, 1998 |