Rotating horizontal convection and the potential vorticity constraint

Horizontal convection, with a focus on the essential physics it can disclose for the oceanic overturning circulation, is studied in an annular gap where differential heating is applied along the bottom. Based on the three-dimensional distribution of both velocity and temperature fields, we propose that in addition to differential buoyancy forcing and diapycnal mixing, potential vorticity (PV) can also be a limiting factor for the overturning circulation by imposing a constraint on the meridional flow. With rotation, flow has to be along PV contours excepting that effects of diffusion or friction exist to break the PV constraint. In the axisymmetric rotating experiment, the flow along isotherms is to zero-order azimuthal, due to the fact that PV varies only along the radial direction. Consequently, the radial flow appears at the next order with much smaller amplitude, leading to a much weaker overturning circulation compared with that of the non-rotating experiment. In the presence of a full radial barrier, the annular gap can be viewed as a four-sided domain with its northern boundary along the inner cylinder, and the meridional flow shows remarkable inhomogeneity in space. In the absence of any background PV gradient, the flow field equilibrates itself to a state where the PV contours above the bottom boundary layer are largely radial, particularly in a sub-region near the western boundary, allowing a relatively strong radial geostrophic flow and greatly strengthening the overturning circulation from the case without the barrier.