Studies of potential vorticity dynamics provide a basis for both understanding and prediction of circulations in ocean and atmosphere. Norman Phillips’ contributions associate basic geophysical fluid dynamics with progress toward the solution of entire problems.

Here we describe some distinct properties of oceanic and atmospheric Rossby waves. Laboratory- and numerical simulations on a polar b-plane and sphere provide animated images of Rossby-wave propagation, geostrophic turbulence/potential-vorticity stirring, barotropization, and resulting bands of zonal acceleration. A prominent polar anticyclonic vortex provides extra ‘PV-elasticity’ and resistance to lateral mixing of polar tracers. In the oceanic case, with the fluid initially at rest, the Green’s function response is explored, highlighting the western-boundary eddy intensification discovered by Phillips. In the atmospheric case, with forced super-rotation and simple mountain topography, we describe a life-cycle of steady Rossby-wave generation, zonal-flow modification and polar-vortex interaction. Upwind- and downwind wakes of the topography generate important transient Rossby waves including ‘Lighthill’ blocking modes, which alter the circulation west of the topography. The storm track/wake in such models provides coherent meridional communication across a range of latitudes, as the Atlantic and Pacific storm tracks connect the subtropics with the high Arctic.