  In the second paper of this series we pursue two objectives. First, in order
to make the code more sensitive to small effects, we remove many approximations
made in Paper I. Second, we include turbulence and rotation in the
two-dimensional framework. The stellar equilibrium is described by means of a
set of five differential equations, with the introduction of a new dependent
variable, namely the perturbation to the radial gravity, that is found when the
non-radial effects are considered in the solution of the Poisson equation;
following the scheme of the first paper, we write the equations in such a way
that the two-dimensional effects can be easily disentangled. The key concept
introduced in this series is the equipotential surface. We use the underlying
cause-effect relation to develop a recurrence relation to calculate the
equipotential surface functions for uniform rotation, differential rotation,
rotation-like toroidal magnetic fields and turbulence. We also develop a more
precise code to numerically solve the two-dimensional stellar structure and
evolution equations based on the equipotential surface calculations. We have
shown that with this formulation we can achieve the precision required by
observations by appropriately selecting the convergence criterion. Several
examples are presented to show that the method works well. Since we are
interested in modeling the effects of a dynamo-type field on the detailed
envelope structure and global properties of the Sun, the code has been
optimized for short timescales phenomena (down to 1 yr). The time dependence of
the code has so far been tested exclusively to address such problems.
