ON THE SOLAR DIFFERENTIAL ROTATION - MERIDIONAL MOTIONS ASSOCIATED WITH A SLOWLY VARYING ANGULAR VELOCITY

The meridional flow in the solar convection zone (SCZ) is calculated from the azimuthal momentum equation, and the results are compared with the existing surface observations. Other than the meridional flow, the azimuthal momentum equation contains the velocity correlations [u(r)u(phi)] and [u(theta)u(phi)], as well as the angular velocity OMEGA. Here u designates the turbulent convective velocities and the brackets denote an appropriate average. The angular velocity is assumed to be a slowly varying function of r, and the velocity correlations are evaluated with the help of a formalism developed previously. The approximations involved in these calculations are the following: let OMEGA = OMEGA0[omega0(r)P0 + omega2(r)P2 + omega4(r)P4 + ...], where the P(n) are Legendre polynomials. The meridional motions can be decomposed into flows with 1, 2, 3, ... cells per hemisphere characterized by their stream functions psi2(r), psi4(r), psi6(r), .... The equations for psi2 and psi4 are solved for the entire SCZ under the assumption that terms of order higher that omega2 and psi4 are small and that omega0, omega2 are constant. It is found that (4/3)psi2 + psi4 almost-equal-to 0 with psi2 < 0: the one-cell meridional flow rises at the equator and sinks at the poles, whereas the two-cell meridional flow sinks at mid-latitudes. The sense of these motions is in agreement with the analysis of GONG's breadboard data and with the motions of weak magnetic features at the solar surface. Furthermore, the rigid rotation of magnetic field patterns at the solar surface allows for an appealing explanation if the one-cell flow is poleward, whereas the pole-equator limb variations in temperature suggest a two-cell flow sinking at mid-latitudes