Following meteorological practice the definition of available potential energy in the ocean is conventionally defined in terms of the properties of the global ocean. However there is also a requirement for a localised definition, for example the energy released when shelf water cascades down a continental shelf in the Arctic and enters a boundary current.

In this note we start from first principals to obtain an exact expression for the available energy (AE) in such a situation. We show that the available energy depends on enstrophy and gravity. We also show that it is exactly equal to the work done by the pressure gradient and by buoyancy.

The results are used to investigate the distribution of AE in the Barents Sea and surrounding regions relative to the interior of the Arctic Ocean. We find that water entering the Barents Sea from the Atlantic already has a high AE, that it is increased by cooling but that much of the increase is lost overcoming turbulence during the passage through the region to the Arctic Ocean. However on entering the Arctic enough available energy remains to drive a significant current around the margin of the ocean. The core of raised available energy also acts as a tracer which can be followed along the continental slope beyond the dateline.