A dynamic equilibrium theory for zonal circulation in the solar convection zone

Recent observations characterize solar shape in terms of a surface radius function composed of Legendre polynomials $P_0, P_2, P_4$, and their amplitudes $a_0, a_2, a_4$. In this work it is assumed the $a_2$ and $a_4$ shape anomaly amplitudes are determined a priori as an energy minimum configuration of the body. The model calculates the poleward pressure gradient forces caused by the shape anomaly.

It separately calculates the equatorward centrifugal forces caused by the rotation of the reference frame. Contrary to expectations, these two forces do not exactly cancel. The residual is identified as the Coriolis force.

The fluid velocity required to close the force budget is the observed zonal circulation. This dynamic equilibrium model offers a new paradigm to explain the zonal circulation of the Sun.