We examine the steady axisymmetric source–sink flows of a stably stratified fluid in a rotating annulus, for which S ∼ O(1), E [Lt ] 1. Numerical methods are used to integrate the unsteady Navier–Stokes equations to obtain the approximate steady solutions. Results on the radial and vertical structures of the flow and temperature-field details are presented. Specific comparisons of the relative sizes of the terms in the equations are conducted to reveal the balance of the dynamic effects. The profiles of the vorticity components are displayed. In the linear flow regime of a homogeneous fluid, the transport of fluid in the meridional plane takes place entirely via boundary layers. As stratification increases, the meridional flows are less concentrated in the boundary layers, and an appreciable portion of the meridional fluid transport is carried through the main body of fluid. The distinction between the sidewall layers and the interior becomes less clear. The flows in the main body of fluid develop vertical velocity shear, resulting in a thermal-wind relation. In the nonlinear case, the source sidewall layer thickens and the sink layer thins. As stratification increases, the meridional fluid transport through the main body of fluid is more pronounced than in the linear case. The balance of terms indicates that the bulk of the flow field is still characterized by the thermal-wind relation.