approximation, similar ideas apply to the mixing of potential vorticity (Wood & McIntyre 2010). In
§2 we consider a Boussinesq fluid with a linear equation of state, and revisit briefly the definition
of available potential energy Ea in a finite volume V and its interpretation in terms of an
adiabatic re-sorting of infinitesimal fluid parcels. In §3 we show that the expression for available
potential energy density of Roullet & Klein (2009) can be written as the sum of two terms: the …