  The first consistent model for the turbulent tachocline is presented, with
the turbulent diffusivity computed within the model instead of being specified
arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed.
Owing to the strongly stable stratification, the mean radial shear is stable,
while the horizontal shear is expected to drive predominantly horizontal,
quasi-2D motions in thin slabs. Here I suggest that a major source of 3D
overturning turbulent motions in the tachocline is the secondary shear
instability due to the strong, random vertical shear arising between the
uncorrelated horizontal flows in neighbouring slabs. A formula for the vertical
diffusivity due to this turbulence, equation (9), is derived and applied in a
simplified 1D model of the tachocline. It is found that Maxwell stresses due to
an oscillatory poloidal magnetic field of a few hundred gauss are able to
confine the tachocline to a thickness below 5 Mm. The integral scale of the 3D
overturning turbulence is the buoyancy scale, on the order of 10 km and its
velocity amplitude is a few m/s, yielding a vertical turbulent diffusivity on
the order of 10^8 cm^2/s.
