Isolated lenses or domes of dense (often cold) bottom water are found in many shelf seas and can be expected to induce significant baroclinic circulations. However, provided they have the correct thermal wind shear, many flow states can support a bottom dome structure, including: (a) an anticyclonically circulating dense dome overlain by a static surface layer or (b) cyclonic surface flow around a static dome. A one-dimensional, two-layer, quasi-geostrophic model is applied to a Gaussian vortex to argue that, on account of bottom friction in shelf seas, the bottom layer will spin down to rest over a time-scale of just a few days and that, due to layer coupling through vortex stretching/compression, cyclonic flow will concentrate in the surface layer. The association of cyclonic surface flow with static, dense domes in shallow seas is supported by reports of tank experiments and by recent observations in a cold pool system in the Irish Sea.