A general criterion for the release of background potential energy through double diffusion

Double diffusion occurs when the fluid density depends on two components that diffuse at different rates (e.g. heat and salt in the ocean). Double diffusion can lead to an up- gradient buoyancy flux and drive motion at the expense of potential energy. Here, we follow the work of Lorenz (1955); Winters et al. (1995) for a single component fluid and define the ‘background’ potential energy (BPE) as the energy associated with an adiabatically sorted density field and derive its budget for a double-diffusive fluid. We find that double diffusion can convert BPE into ‘available’ potential energy (APE), unlike in a single-component fluid where the transfer of APE to BPE is irreversible. We also derive an evolution equation for the sorted buoyancy in a double-diffusive fluid, extending the work of Winters & D’Asaro (1996); Nakamura (1996). The criterion we develop for a release of BPE can be used to analyze the energetics of mixing and double diffusion in the ocean and other multiple component fluids, and we illustrate its application using 2D simulations of salt fingering