• Vertically integrated planetary-geostrophic equations, or a homogeneous fluid with nonlinearity neglected
• Friction parameterized by a linear drag (Stommel model) or a harmonic Newtonian viscosity (Munk model) or both (Stommel–Munk model)
• Flat bottomed ocean

Variations on the theme include allowing nonlinearity in the vorticity equation, posing the problem in domains of various shapes, and allowing bottom topography (in particular sloping sidewalls). The solutions are normally calculated in the boundary-layer approximation, but some exact solutions exist.