There are two typos in equation (16) which expresses the radial velocity component in terms of the streamfunctions: 1) The first term should be proportional to 1/r^2, not 1/r 2) The second term should involve the W streamfunction instead of the Z streamfunction.
There are two completely equivalent errors in Equation (22) which expresses the radial component of the magnetic field in terms of the fluxfunctions.
There are two typos in equation (16) which expresses the radial velocity component in terms of the streamfunctions: 1) The first term should be proportional to 1/r^2, not 1/r 2) The second term should involve the W streamfunction instead of the Z streamfunction.
There are two completely equivalent errors in Equation (22) which expresses the radial component of the magnetic field in terms of the fluxfunctions.