Solar Tachocline Revisited

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Abstract
Using recent helioseismological data, Kosovichev has shown that half of the tachocline lies within the convective zone (CZ). Previous theoretical models suggested that it lies outside the CZ. We propose a new model whereby the tachocline originates within the CZ and/or in that part of the overshooting region where the convective flux is still positive. The key ingredients of the model are shear, vorticity, and buoyancy. We find that (1) shear alone, (2) shear + vorticity, and (3) shear + buoyancy are unable to reproduce the measured Reynolds stresses at the surface of the Sun. The key ingredients are vorticity + buoyancy, both of which are missing in previous models. Without carrying out a detailed numerical calculation, we estimate the thickness of the tachocline to be 0.053 (in units of the solar radius) compared with Kosovichev's value of 0.09±0.04. The next step is the numerical solution of the equations.