Available potential energy ($A$)

The portion of a fluid system's potential energy that can be released by admissible rearrangement relative to a stable reference state. In a uniformly stratified incompressible fluid, the quadratic density is $A={\rho }_0{N}^2{\xi }_z^2/2={\rho }_0{b}^2/(2N^2)$, where ${\xi }_z$ is vertical fluid displacement and $b$ the buoyancy perturbation. It is positive for stable stratification and measures the restoring energy of internal gravity waves.

The background potential energy is the gravitational potential energy of the statically stable state obtained by adiabatically sorting a fluid's parcels. The difference $A=P-P_b$ is available potential energy. Pure rearrangement changes $A$ but not $P_b$; irreversible density mixing can increase $P_b$. Molecular exchange with internal energy must be separated when defining an irreversible mixing rate.