  We provide a consistent theory of the tachocline confinement (or anisotropic
momentum transport) within an hydrodynamical turbulence model. The goal is to
explain helioseismological data, which show that the solar tachocline thickness
is at most 5% of the solar radius, despite the fact that, due to radiative
spreading, this transition layer should have thickened to a much more
significant value during the sun's evolution. Starting from the first principle
with the physically plausible assumption that turbulence is driven externally
(e.g. by plumes penetrating from the convection zone), we derive turbulent
(eddy) viscosity in the radial (vertical) and azimuthal (horizontal) directions
by incorporating the crucial effects of shearing due to radial and latitudinal
differential rotations in the tachocline. We show that the simultaneous
presence of both shears induces effectively a much more efficient momentum
transport in the horizontal plane than in the radial direction. In particular,
in the case of strong radial turbulence (driven by overshooting plumes from the
convection zone), the ratio of the radial to horizontal eddy viscosity is
proportional to ${\cal A}^{-1/3}$, where ${\cal A}$ is the strength of the
shear due to radial differential rotation. In comparison, in the case of
horizontally driven turbulence, this ratio becomes of order $-\epsilon^2$, with
negative radial eddy viscosity. Here, $\epsilon$ ($\ll 1$) is the ratio of the
radial to latitudinal shear. The resulting anisotropy in momentum transport
could thus be sufficiently strong to operate as a mechanism for the tachocline
confinement against spreading.
