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

This work proposes a new theoretical model for the observed differential zonal motion in the solar convection zone. It is based on a dynamic equilibrium among three fundamental forces: pressure gradient forces, centrifugal forces, and Coriolis forces. Existing models, many achieving substantial success, require convection as a key mechanism to drive the zonal motion. Generally these models have a geostrophic balance as their lowest order balance. In the new approach presented here, an even lower order balance is derived and convection is not required. The precise observed shape of the Sun is treated as a fixed boundary condition. 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.